wanyu/IteraTeR_v2 huggingface dataset:
Original: Due to the singularity of the logarithmic function, it introduces tremendous difficulties in establishing mathematical theories and in designing and analyzing numerical methods for PDEs with logarithmic nonlinearity.
Revised: Due to the singularity of the logarithmic function, it introduces tremendous difficulties in establishing mathematical theories , as well asin designing and analyzing numerical methods for PDEs with logarithmic nonlinearity.
Edit intent: coherence
Original: Due to the singularity of the logarithmic function, it introduces tremendous difficulties in establishing mathematical theories and in designing and analyzing numerical methods for PDEs with logarithmic nonlinearity.
Revised: Due to the singularity of the logarithmic function, it introduces tremendous difficulties in establishing mathematical theories and in designing and analyzing numerical methods for PDEs with such nonlinearity.
Edit intent: clarity
Original:  Here we take the logarithmic Schr \"o%DIFDELCMD < }%%% dinger equation (LogSE)as a prototype model.
Revised:  Here we take the logarithmic \"o%DIFDELCMD < }%%% dinger equation (LogSE)as a prototype model.
Edit intent: fluency
Original:  Here we take the logarithmic Schr \"o%DIFDELCMD < }%%% dinger equation (LogSE)as a prototype model.
Revised:  Here we take the logarithmic Schr %DIFDELCMD < }%%% dinger equation (LogSE)as a prototype model.
Edit intent: fluency
Original:  Here we take the logarithmic Schr \"o%DIFDELCMD < }%%% dinger equation (LogSE)as a prototype model.
Revised:  Here we take the logarithmic Schr \"o%DIFDELCMD < }%%% Schr\"odinger equation (LogSE)as a prototype model.
Edit intent: fluency
Original:  Instead of regularizing f(\rho)= ln \rho in the LogSE directly as being done in the literature, we propose an energy regularization for the LogSE by first regularizing F(\rho)=\rho ln \rho -- \rho near \rho=0 + with a polynomial approximation in the energy functional of the LogSE and then obtaining an energy regularized logarithmic Schr \"o%DIFDELCMD < }%%% dinger equation (ERLogSE) via energy variation.
Revised:  Instead of regularizing f(\rho)= ln \rho in the LogSE directly as being done in the literature, we propose an energy regularization for the LogSE byfirst regularizing F(\rho)=\rho ln \rho -- \rho near \rho=0 + with a polynomial approximation in the energy functional of the LogSE and then obtaining an energy regularized logarithmic Schr \"o%DIFDELCMD < }%%% dinger equation (ERLogSE) via energy variation.
Edit intent: fluency
Original:  Instead of regularizing f(\rho)= ln \rho in the LogSE directly as being done in the literature, we propose an energy regularization for the LogSE by first regularizing F(\rho)=\rho ln \rho -- \rho near \rho=0 + with a polynomial approximation in the energy functional of the LogSE and then obtaining an energy regularized logarithmic Schr \"o%DIFDELCMD < }%%% dinger equation (ERLogSE) via energy variation.
Revised:  Instead of regularizing f(\rho)= ln \rho in the LogSE directly as being done in the literature, we propose an energy regularization for the LogSE by first regularizing F(\rho)=\rho ln \rho -- \rho near \rho=0 ^+ with a polynomial approximation in the energy functional of the LogSE and then obtaining an energy regularized logarithmic Schr \"o%DIFDELCMD < }%%% dinger equation (ERLogSE) via energy variation.
Edit intent: clarity
Original:  Instead of regularizing f(\rho)= ln \rho in the LogSE directly as being done in the literature, we propose an energy regularization for the LogSE by first regularizing F(\rho)=\rho ln \rho -- \rho near \rho=0 + with a polynomial approximation in the energy functional of the LogSE and then obtaining an energy regularized logarithmic Schr \"o%DIFDELCMD < }%%% dinger equation (ERLogSE) via energy variation.
Revised:  Instead of regularizing f(\rho)= ln \rho in the LogSE directly as being done in the literature, we propose an energy regularization for the LogSE by first regularizing F(\rho)=\rho ln \rho -- \rho near \rho=0 + with a polynomial approximation in the energy functional of the LogSE and then obtaining an energy regularized logarithmic \"o%DIFDELCMD < }%%% dinger equation (ERLogSE) via energy variation.
Edit intent: fluency
Original:  Instead of regularizing f(\rho)= ln \rho in the LogSE directly as being done in the literature, we propose an energy regularization for the LogSE by first regularizing F(\rho)=\rho ln \rho -- \rho near \rho=0 + with a polynomial approximation in the energy functional of the LogSE and then obtaining an energy regularized logarithmic Schr \"o%DIFDELCMD < }%%% dinger equation (ERLogSE) via energy variation.
Revised:  Instead of regularizing f(\rho)= ln \rho in the LogSE directly as being done in the literature, we propose an energy regularization for the LogSE by first regularizing F(\rho)=\rho ln \rho -- \rho near \rho=0 + with a polynomial approximation in the energy functional of the LogSE and then obtaining an energy regularized logarithmic Schr %DIFDELCMD < }%%% dinger equation (ERLogSE) via energy variation.
Edit intent: clarity
Original:  Instead of regularizing f(\rho)= ln \rho in the LogSE directly as being done in the literature, we propose an energy regularization for the LogSE by first regularizing F(\rho)=\rho ln \rho -- \rho near \rho=0 + with a polynomial approximation in the energy functional of the LogSE and then obtaining an energy regularized logarithmic Schr \"o%DIFDELCMD < }%%% dinger equation (ERLogSE) via energy variation.
Revised:  Instead of regularizing f(\rho)= ln \rho in the LogSE directly as being done in the literature, we propose an energy regularization for the LogSE by first regularizing F(\rho)=\rho ln \rho -- \rho near \rho=0 + with a polynomial approximation in the energy functional of the LogSE and then obtaining an energy regularized logarithmic Schr \"o%DIFDELCMD < }%%% Schr\"odinger equation (ERLogSE) via energy variation.
Edit intent: fluency
Original:  Linear convergence is established between the solutions of ERLogSE and LogSE in terms of a small regularization parameter 0< \epsilon \ll 1. \ep\ll1 Moreover,
Revised:  Linear convergence is established between the solutions of ERLogSE and LogSE in terms of a small regularization parameter 0< \epsilon \ll 1. \ep\ll1. Moreover,
Edit intent: fluency
Original:  the conserved energy of the ERLogSE converges to that of LogSE quadratically  . Error estimates are also established for solving the ERLogSE by using Lie-Trotter splitting integrators . Numerical results are reported to confirm our error estimates of the energy reg-ularization and of the time-splitting integrators for the ERLogSE . Finally our results suggest that energy regularization performs better than regularizing the logarithmic nonlinearity in the LogSE directly.
Revised:  the conserved energy of the ERLogSE converges to that of LogSE quadratically . Error estimates are alsopresented for solving the ERLogSE by using Lie-Trotter splitting integrators . Numerical results are reported to confirm our error estimates of the energy reg-ularization and of the time-splitting integrators for the ERLogSE . Finally our results suggest that energy regularization performs better than regularizing the logarithmic nonlinearity in the LogSE directly.
Edit intent: clarity
Original:  the conserved energy of the ERLogSE converges to that of LogSE quadratically  . Error estimates are also established for solving the ERLogSE by using Lie-Trotter splitting integrators . Numerical results are reported to confirm our error estimates of the energy reg-ularization and of the time-splitting integrators for the ERLogSE . Finally our results suggest that energy regularization performs better than regularizing the logarithmic nonlinearity in the LogSE directly.
Revised:  the conserved energy of the ERLogSE converges to that of LogSE quadratically . Error estimates are also established for solving the ERLogSE by using Lie-Trotter splittingintegrators . Numerical results are reported to confirm our error estimates of the energy reg-ularization and of the time-splitting integrators for the ERLogSE . Finally our results suggest that energy regularization performs better than regularizing the logarithmic nonlinearity in the LogSE directly.
Edit intent: fluency
Original:  the conserved energy of the ERLogSE converges to that of LogSE quadratically  . Error estimates are also established for solving the ERLogSE by using Lie-Trotter splitting integrators . Numerical results are reported to confirm our error estimates of the energy reg-ularization and of the time-splitting integrators for the ERLogSE . Finally our results suggest that energy regularization performs better than regularizing the logarithmic nonlinearity in the LogSE directly.
Revised:  the conserved energy of the ERLogSE converges to that of LogSE quadratically . Error estimates are also established for solving the ERLogSE by using Lie-Trotter splitting integrators . Numerical results are reported to confirm our errorestimates of the LER and of the time-splitting integrators for the ERLogSE . Finally our results suggest that energy regularization performs better than regularizing the logarithmic nonlinearity in the LogSE directly.
Edit intent: clarity
Original:  the conserved energy of the ERLogSE converges to that of LogSE quadratically  . Error estimates are also established for solving the ERLogSE by using Lie-Trotter splitting integrators . Numerical results are reported to confirm our error estimates of the energy reg-ularization and of the time-splitting integrators for the ERLogSE . Finally our results suggest that energy regularization performs better than regularizing the logarithmic nonlinearity in the LogSE directly.
Revised:  the conserved energy of the ERLogSE converges to that of LogSE quadratically . Error estimates are also established for solving the ERLogSE by using Lie-Trotter splitting integrators . Numerical results are reported to confirm our error estimates of the energy reg-ularization and of the time-splitting integrators for theERLogSE . Finally our results suggest that energy regularization performs better than regularizing the logarithmic nonlinearity in the LogSE directly.
Edit intent: fluency
Original: In this paper, we seek to reduce the computation complexity of transformer-based models for speech representation learning.
Revised: In this paper, we seek solutions for reducing the computation complexity of transformer-based models for speech representation learning.
Edit intent: clarity
Original:  We evaluate 10 attention mechanisms ;
Revised:  We evaluate 10 attention algorithms ;
Edit intent: clarity
Original:  then, we pre-train the transformer-based model with those attentions in a self-supervised fashion and use them as feature extractors on downstream tasks, including phoneme classification and speaker classification.
Revised:  then, we pre-train the transformer-based model with those attention algorithms in a self-supervised fashion and use them as feature extractors on downstream tasks, including phoneme classification and speaker classification.
Edit intent: clarity
Original:  then, we pre-train the transformer-based model with those attentions in a self-supervised fashion and use them as feature extractors on downstream tasks, including phoneme classification and speaker classification.
Revised:  then, we pre-train the transformer-based model with those attentions in a self-supervised fashion and treat them as feature extractors on downstream tasks, including phoneme classification and speaker classification.
Edit intent: clarity
Original:  PayloadPark forwards only the packet headers to the NF serversand saves transmit and receive bandwidth between the switch and the NF server.
Revised:  PayloadPark forwards only packet headers to the NF serversand saves transmit and receive bandwidth between the switch and the NF server.
Edit intent: clarity
Original:  PayloadPark forwards only the packet headers to the NF serversand saves transmit and receive bandwidth between the switch and the NF server.
Revised:  PayloadPark forwards only the packet headers to NF servers, thereby saving bandwidth between the switch and the NF server.
Edit intent: clarity
Original:  The prototype improves goodput by 10-36 \% for Firewall and NAT NFs and by 10-26\% for a Firewall -> NAT NF chain without harming latency.
Revised:  The prototype improves goodput by 10- 36 \% for Firewall and NAT NFs and by 10-26\% for a Firewall -> NAT NF chain without harming latency.
Edit intent: fluency
Original:  The prototype also saves 2-58\% of the PCIe bandwidth on the NF server thanks to the reduced data transmission between the switch and the NF server.
Revised:  The prototype also saves 2-58\% on the NF server thanks to the reduced data transmission between the switch and the NF server.
Edit intent: clarity
Original:  (3) the object is  awarded to the agent with the highest score, provided it 's nonnegative;
Revised:  (3) the object is such that the object should be awarded to the agent with the highest score, provided it 's nonnegative;
Edit intent: clarity
Original:  The situation just described constitutes a social dilemma---namely , a situation where no one has an individual incentive to cooperate, though mutual cooperation would lead to the best outcome for all involved.
Revised:  The situation just described constitutes a social dilemma; namely , a situation where no one has an individual incentive to cooperate, though mutual cooperation would lead to the best outcome for all involved.
Edit intent: fluency
Original:  The annotations can easily be exported in JSON format for further processing .
Revised:  The annotations can easily be exported in JSON format for further analysis .
Edit intent: clarity
Original:  Here we want to study the question if we loose much from a practical point of view, if we restrict ourselves to weighted games.
Revised:  Here we want to study the question if we lose much from a practical point of view, if we restrict ourselves to weighted games.
Edit intent: fluency
Original: Measures to reduce the impact of COVID19 require a mix of logistic, political and social capacity.
Revised: Measures to reduce the impact of the COVID-19 pandemic require a mix of logistic, political and social capacity.
Edit intent: clarity
Original:  Depending on the country, different capacities to increase of hospitalization or to properly apply lockdowns are observed.
Revised:  Depending on the country, different approaches to increase hospitalization capacity or to properly apply lockdowns are observed.
Edit intent: clarity
Original:  Depending on the country, different capacities to increase of hospitalization or to properly apply lockdowns are observed.
Revised:  Depending on the country, different capacities to increase of hospitalization or to properly apply lock-downs are observed.
Edit intent: fluency
Original: Bayesian quadrature (BQ) is a method for solving numerical integration problems in a Bayesian manner, which allows user to quantify their uncertainty about the solution.
Revised: Bayesian quadrature (BQ) is a method for solving numerical integration problems in a Bayesian manner, which allows users to quantify their uncertainty about the solution.
Edit intent: fluency
Original:  The standard approach to BQ is based on  Gaussian process (GP) approximation of the integrand.
Revised:  The standard approach to BQ is based on a Gaussian process (GP) approximation of the integrand.
Edit intent: fluency
Original:  As a result, BQ approach is inherently limited to cases where GP approximations can be done in an efficient manner, thus often prohibiting  high-dimensional or non-smooth target functions.
Revised:  As a result, BQ is inherently limited to cases where GP approximations can be done in an efficient manner, thus often prohibiting high-dimensional or non-smooth target functions.
Edit intent: clarity
Original: A modal logic is non-iterative if it can be defined by axioms that do not nest modal operators, and rank-1 if additionally all propositional variables in axioms are in scope of a modal operator.
Revised: A modal logic is non-iterative if it can be defined by axioms that do not nest modal operators, and rank-1 if additionally all propositional variables in axioms are in scope of a modal operator.
Edit intent: fluency
Original:  Like in the rank-1 case, the  coalgebraic semantics is equivalent to a neighbourhood semantics with suitable frame conditions, so that our main result may be phrased as saying that every non-iterative modal logic is complete over its neighbourhood semantics .
Revised:  Like in the rank-1 case, the coalgebraic semantics is equivalent to a neighbourhood semantics with suitable frame conditions, so that our main result may be phrased as saying that every non-iterative modal logics over neighbourhood semantics is implied .
Edit intent: clarity
Original:  As an example application of these results, we establish strong completeness of deontic logics with factual detachment, strengthening previous weak completeness results.
Revised:  As an illustration of these results, we establish strong completeness of deontic logics with factual detachment, strengthening previous weak completeness results.
Edit intent: clarity
Original:  As an example application of these results, we establish strong completeness of deontic logics with factual detachment, strengthening previous weak completeness results.
Revised:  As an example application of these results, we discuss deontic logics with factual detachment, strengthening previous weak completeness results.
Edit intent: clarity
Original: Learning 3D geometry directly from raw data, such as point clouds, triangle soups, or un-oriented meshes is still a challenging task that feeds many downstream computer vision and graphics applications.
Revised: Learning 3D geometry directly from raw data, such as point clouds, triangle soups, or unoriented meshes is still a challenging task that feeds many downstream computer vision and graphics applications.
Edit intent: fluency
Original:  In this paper, we introduce SAL++ : a method for learning implicit neural representations of shapes directly from such raw data.
Revised:  In this paper, we introduce SAL++ : a method for learning implicit neural representations of shapes directly from raw data.
Edit intent: clarity
Original:  We build upon the recent sign agnostic learning (SAL) approach and generalize it to include derivative data in a sign agnostic manner.
Revised:  We generalize sign agnostic learning (SAL) approach and generalize it to include derivative data in a sign agnostic manner.
Edit intent: clarity
Original:  In more detail, given the unsigned distance function to the input raw data, we suggest a novel sign agnostic regression loss, incorporating both pointwise values and gradients of the unsigned distance function.
Revised:  In more detail, given the unsigned distance function to the input raw data, we advocate a novel sign agnostic regression loss, incorporating both pointwise values and gradients of the unsigned distance function.
Edit intent: clarity
Original:  Optimizing this loss leads to a signed implicit function solution, the zero level set of which is a high quality , valid manifold approximation to the input 3D data.
Revised:  Optimizing this loss leads to a signed implicit function solution, the zero level set of which is a high quality and valid manifold approximation to the input 3D data.
Edit intent: fluency
Original:   We demonstrate the efficacy of SAL++ shape space learning from two challenging datasets: ShapeNet that contains inconsistent orientation and non-manifold meshes, and D-Faust that contains raw 3D scans (triangle soups).
Revised:  We demonstrate the efficacy of SALD for shape space learning from two challenging datasets: ShapeNet that contains inconsistent orientation and non-manifold meshes, and D-Faust that contains raw 3D scans (triangle soups).
Edit intent: clarity
Original:   We demonstrate the efficacy of SAL++ shape space learning from two challenging datasets: ShapeNet that contains inconsistent orientation and non-manifold meshes, and D-Faust that contains raw 3D scans (triangle soups).
Revised:  We demonstrate the efficacy of SAL++ shape space learning on two challenging datasets: ShapeNet that contains inconsistent orientation and non-manifold meshes, and D-Faust that contains raw 3D scans (triangle soups).
Edit intent: fluency
Original: The recent advent of single cell RNA-sequencing and other high-throughput technologies has led to an explosion of cell type definitions across multiple organ systems.
Revised: The advancement of single cell RNA-sequencing and other high-throughput technologies has led to an explosion of cell type definitions across multiple organ systems.
Edit intent: clarity
Original: The recent advent of single cell RNA-sequencing and other high-throughput technologies has led to an explosion of cell type definitions across multiple organ systems.
Revised: The recent advent of single cell RNA-sequencing technologies has led to an explosion of cell type definitions across multiple organ systems.
Edit intent: clarity
Original:  however, the naming and organization of cell types has largely been left to individual investigators, resulting in widely varying nomenclature and limited alignment between taxonomies derived from overlapping datasets .
Revised:  however, the naming and organization of cell types has largely been left to individual investigators, resulting in widely varying nomenclature and limited alignment between taxonomies .
Edit intent: clarity
Original:  Finally, we propose conventions for assigning accurate yet flexible cell types names in the mammalian cortex as a step towards a much larger community-wide effort to organize multi-source, data-driven information related to cell types.
Revised:  The CCN facilitates assigning accurate yet flexible cell types names in the mammalian cortex as a step towards a much larger community-wide effort to organize multi-source, data-driven information related to cell types.
Edit intent: clarity
Original:  Finally, we propose conventions for assigning accurate yet flexible cell types names in the mammalian cortex as a step towards a much larger community-wide effort to organize multi-source, data-driven information related to cell types.
Revised:  Finally, we propose conventions for assigning accurate yet flexible cell type names in the mammalian cortex as a step towards a much larger community-wide effort to organize multi-source, data-driven information related to cell types.
Edit intent: fluency
Original:  Finally, we propose conventions for assigning accurate yet flexible cell types names in the mammalian cortex as a step towards a much larger community-wide effort to organize multi-source, data-driven information related to cell types.
Revised:  Finally, we propose conventions for assigning accurate yet flexible cell types names in the mammalian cortex as a step towards community-wide effort to organize multi-source, data-driven information related to cell types.
Edit intent: clarity
Original:  Finally, we propose conventions for assigning accurate yet flexible cell types names in the mammalian cortex as a step towards a much larger community-wide effort to organize multi-source, data-driven information related to cell types.
Revised:  Finally, we propose conventions for assigning accurate yet flexible cell types names in the mammalian cortex as a step towards a much larger community-wide efforts to organize multi-source, data-driven information related to cell types.
Edit intent: fluency
Original:  The convention presented here can be easily applied to cell type taxonomies from any organ system or organism.
Revised:  The convention presented here can be easily applied to cell type taxonomies from any organism.
Edit intent: clarity
Original:  Recently we have proposed a temporal multiscale method that fits into the framework of the heterogeneous multiscale method and that allows for efficient simulations with significant speedups.
Revised:  Recently we have proposed a temporal multiscale approach that fits into the framework of the heterogeneous multiscale method and that allows for efficient simulations with significant speedups.
Edit intent: clarity