wanyu/IteraTeR_v2 huggingface dataset:
Original:  To evaluate the functional organization in multi-task deep neural networks  we propose a method that measures the contribution of a unit towards each task and apply it to two networks that have been trained on either two related or two unrelated tasks  using an identical stimulus set.
Revised:  To evaluate the functional organization in multi-task deep neural networks we propose a method that measures the contribution of a unit towards each task , applying it to two networks that have been trained on either two related or two unrelated tasks using an identical stimulus set.
Edit intent: coherence
Original:  To evaluate the functional organization in multi-task deep neural networks  we propose a method that measures the contribution of a unit towards each task and apply it to two networks that have been trained on either two related or two unrelated tasks  using an identical stimulus set.
Revised:  To evaluate the functional organization in multi-task deep neural networks we propose a method that measures the contribution of a unit towards each task and apply it to two networks that have been trained on either two related or two unrelated tasks , using an identical stimulus set.
Edit intent: fluency
Original:  We conjecture that the method we propose can be used to reason about the anatomical and functional organization of the visual system and beyond as we predict that the degree to which tasks are related is a good descriptor of the degree to which they can share downstream cortical-units.
Revised:  We conjecture that the method we propose can be used to analyze the anatomical and functional organization of the visual system and beyond as we predict that the degree to which tasks are related is a good descriptor of the degree to which they can share downstream cortical-units.
Edit intent: clarity
Original:  We conjecture that the method we propose can be used to reason about the anatomical and functional organization of the visual system and beyond as we predict that the degree to which tasks are related is a good descriptor of the degree to which they can share downstream cortical-units.
Revised:  We conjecture that the method we propose can be used to reason about the anatomical and functional organization of the visual system and beyond . We predict that the degree to which tasks are related is a good descriptor of the degree to which they can share downstream cortical-units.
Edit intent: coherence
Original:  We conjecture that the method we propose can be used to reason about the anatomical and functional organization of the visual system and beyond as we predict that the degree to which tasks are related is a good descriptor of the degree to which they can share downstream cortical-units.
Revised:  We conjecture that the method we propose can be used to reason about the anatomical and functional organization of the visual system and beyond as we predict that the degree to which tasks are related is a good descriptor of the degree to which they share downstream cortical-units.
Edit intent: clarity
Original: We study an optimal dividend problem under a bankruptcy constraint where firms face a trade-off between potential bankruptcy and extraction of owner profits.
Revised: We study an optimal dividend problem under a bankruptcy constraint . Firms face a trade-off between potential bankruptcy and extraction of owner profits.
Edit intent: coherence
Original: We study an optimal dividend problem under a bankruptcy constraint where firms face a trade-off between potential bankruptcy and extraction of owner profits.
Revised: We study an optimal dividend problem under a bankruptcy constraint where firms face a trade-off between potential bankruptcy and extraction of profits.
Edit intent: clarity
Original:  In contrast to previous works, more general cash flow drifts, including Ornstein--Uhlenbeck and CIR processes, are considered.
Revised:  In contrast to previous works, general cash flow drifts, including Ornstein--Uhlenbeck and CIR processes, are considered.
Edit intent: clarity
Original:  Finally, we present and numerically study extensions of the model, such as equity issuance and lotteries .
Revised:  Finally, we present and numerically study extensions of the model, including equity issuance and lotteries .
Edit intent: style
Original:  The value function is thus given by a nonlinear PDE with a gradient constraint from below in one dimension.
Revised:  The value function is given by a nonlinear PDE with a gradient constraint from below in one dimension.
Edit intent: coherence
Original: Network embedding leverages the node proximity manifested to learn a low-dimensional node vector representation  .
Revised: Network embedding leverages the node proximity manifested to learn a low-dimensional node vector representation for each node in the network .
Edit intent: clarity
Original:  Most, if not all, of the existing work, is overwhelmingly performed in the context of plain and static networks.
Revised:  Most, if not all, of the existing works, are overwhelmingly performed in the context of plain and static networks.
Edit intent: fluency
Original:  Also, a vast majority of real-world networks are associated with a rich set of node attributes, and their attribute values are also naturally changing, with the emerging of new content  and the fading of old content  .
Revised:  Also, a vast majority of real-world networks are associated with a rich set of node attributes, and their attribute values are also naturally changing, with the emerging of new content patterns and the fading of old content .
Edit intent: clarity
Original:  Also, a vast majority of real-world networks are associated with a rich set of node attributes, and their attribute values are also naturally changing, with the emerging of new content  and the fading of old content  .
Revised:  Also, a vast majority of real-world networks are associated with a rich set of node attributes, and their attribute values are also naturally changing, with the emerging of new content and the fading of old content patterns .
Edit intent: clarity
Original:  In particular, DANE  provides an offline method for a consensus embedding first and then leverages matrix perturbation theory to maintain the freshness of the end embedding results in an online manner.
Revised:  In particular, DANE first provides an offline method for a consensus embedding first and then leverages matrix perturbation theory to maintain the freshness of the end embedding results in an online manner.
Edit intent: fluency
Original:  In particular, DANE  provides an offline method for a consensus embedding first and then leverages matrix perturbation theory to maintain the freshness of the end embedding results in an online manner.
Revised:  In particular, DANE provides an offline method for a consensus embedding and then leverages matrix perturbation theory to maintain the freshness of the end embedding results in an online manner.
Edit intent: coherence
Original: Drug-target interaction (DTI) prediction plays a very important role in drug development  . Biochemical experiments or in vitro methods to identify such interactions  are very expensive, laborious and time-consuming.
Revised: Drug-target interaction (DTI) prediction plays a very important role in drug development . Biochemical experiments or in vitro are very expensive, laborious and time-consuming.
Edit intent: clarity
Original: Drug-target interaction (DTI) prediction plays a very important role in drug development  . Biochemical experiments or in vitro methods to identify such interactions  are very expensive, laborious and time-consuming.
Revised: Drug-target interaction (DTI) prediction plays a very important role in drug development . Biochemical experiments or in vitro methods to identify such interactions methods are very expensive, laborious and time-consuming.
Edit intent: fluency
Original:  Therefore, in silico \textit{ approaches including docking simulation and machine learning have been proposed to solve this problem.
Revised:  Therefore, \textit{ approaches including docking simulation and machine learning have been proposed to solve this problem.
Edit intent: clarity
Original:  In this paper, we will introduce a new Chemical Kinetics Experimental Data format, ChemKED, and the related Python-based package for creating and validating ChemKED-formatted files called PyKED.
Revised:  In this paper, we introduce a new Chemical Kinetics Experimental Data format, ChemKED, and the related Python-based package for creating and validating ChemKED-formatted files called PyKED.
Edit intent: coherence
Original:  ChemKED-formatted files contain all of the information needed to simulate experimental data points, including uncertainty .
Revised:  ChemKED-formatted files contain all of the information needed to simulate experimental data points, including the uncertainty of the data .
Edit intent: clarity
Original: Fundamental experimental measurements of quantities including ignition delay times, laminar flame speeds, and species profiles  serve important roles in understanding fuel chemistry and validating chemical kinetic models.
Revised: Fundamental experimental measurements of quantities such as ignition delay times, laminar flame speeds, and species profiles serve important roles in understanding fuel chemistry and validating chemical kinetic models.
Edit intent: fluency
Original:  In this paper, we introduce a new Chemical Kinetics Experimental Data format, ChemKED, and the related Python-based package for creating and validating ChemKED-formatted files called PyKED.
Revised:  Here we introduce a new Chemical Kinetics Experimental Data format, ChemKED, and the related Python-based package for creating and validating ChemKED-formatted files called PyKED.
Edit intent: clarity
Original:  In this paper, we introduce a new Chemical Kinetics Experimental Data format, ChemKED, and the related Python-based package for creating and validating ChemKED-formatted files called PyKED.
Revised:  In this paper, we introduce a new chemical kinetics experimental data format, ChemKED, and the related Python-based package for creating and validating ChemKED-formatted files called PyKED.
Edit intent: fluency
Original:  In this paper, we introduce a new Chemical Kinetics Experimental Data format, ChemKED, and the related Python-based package for creating and validating ChemKED-formatted files called PyKED.
Revised:  In this paper, we introduce a new Chemical Kinetics Experimental Data format, ChemKED, and the related Python-based package for validating and working with ChemKED-formatted files called PyKED.
Edit intent: clarity
Original:  We will also review past and related efforts, and motivate the need for a new solution.
Revised:  We also review past and related efforts, and motivate the need for a new solution.
Edit intent: fluency
Original:  Plans for future development include support for experimental data from  jet stirred reactor , extinction , and speciation measurements.
Revised:  Plans for future development include support for experimental data from jet stirred reactor , and speciation measurements.
Edit intent: clarity
Original: Recently, the k-induction algorithm has proven to be a successful approach for both finding bugs and proving correctness in program verification .
Revised: Recently, the k-induction algorithm has proven to be a successful approach for both finding bugs and proving correctness .
Edit intent: clarity
Original:  In this paper, we suggest an extension to the k-induction algorithm , which uses the counterexample produced from over-approximating the loops occurring in the program, in order to shorten the number of steps required to find bugs.
Revised:  In this paper, we propose to extend the k-induction algorithm , which uses the counterexample produced from over-approximating the loops occurring in the program, in order to shorten the number of steps required to find bugs.
Edit intent: clarity
Original:  In this paper, we suggest an extension to the k-induction algorithm , which uses the counterexample produced from over-approximating the loops occurring in the program, in order to shorten the number of steps required to find bugs.
Revised:  In this paper, we suggest an extension to the k-induction algorithm in order to shorten the number of steps required to find bugs.
Edit intent: coherence
Original:  For covariance functions that are Green's functions  elliptic boundary value problems and approximately equally spaced sampling points, we show how to identify a subset S \subset \{ 1 , \dots , N \} \times \{ 1 , \dots , N \}, with \# S = O ( N \log (N) \log^{d} ( N /\epsilon ) ), such that the zero fill-in block-incomplete Cholesky decomposition of i,j 1 _{( i, j ) \in S} is an \epsilon-approximation of \Theta.
Revised:  For covariance functions that are Green's functions of elliptic boundary value problems and approximately equally spaced sampling points, we show how to identify a subset S \subset \{ 1 , \dots , N \} \times \{ 1 , \dots , N \}, with \# S = O ( N \log (N) \log^{d} ( N /\epsilon ) ), such that the zero fill-in block-incomplete Cholesky decomposition of i,j 1 _{( i, j ) \in S} is an \epsilon-approximation of \Theta.
Edit intent: fluency
Original:  For covariance functions that are Green's functions  elliptic boundary value problems and approximately equally spaced sampling points, we show how to identify a subset S \subset \{ 1 , \dots , N \} \times \{ 1 , \dots , N \}, with \# S = O ( N \log (N) \log^{d} ( N /\epsilon ) ), such that the zero fill-in block-incomplete Cholesky decomposition of i,j 1 _{( i, j ) \in S} is an \epsilon-approximation of \Theta.
Revised:  For covariance functions that are Green's functions elliptic boundary value problems and approximately equally spaced sampling points, we show how to identify a subset S \subset \{ 1 , \dots , N \} \times \{ 1 , \dots , N \}, with \# S = O ( N \log (N) \log^{d} ( N /\epsilon ) ), such that the zero fill-in incomplete Cholesky factorisation of i,j 1 _{( i, j ) \in S} is an \epsilon-approximation of \Theta.
Edit intent: clarity
Original:  This block-factorisation can provably be obtained in O%DIFDELCMD < \left(%%% N \log^{2 ( N \log} ( N ) %DIFDELCMD < \left( %%% \log(1 /\epsilon) + \log^{2 ( N ) }%DIFDELCMD < \right)%%% ^{4d+1 }%DIFDELCMD < \right) %%% complexity in time.
Revised:  This block-factorisation can provably be obtained in %DIFDELCMD < \left(%%% N \log^{2 ( N \log} ( N ) %DIFDELCMD < \left( %%% \log(1 /\epsilon) + \log^{2 ( N ) }%DIFDELCMD < \right)%%% ^{4d+1 }%DIFDELCMD < \right) %%% complexity in time.
Edit intent: clarity
Original:  This block-factorisation can provably be obtained in O%DIFDELCMD < \left(%%% N \log^{2 ( N \log} ( N ) %DIFDELCMD < \left( %%% \log(1 /\epsilon) + \log^{2 ( N ) }%DIFDELCMD < \right)%%% ^{4d+1 }%DIFDELCMD < \right) %%% complexity in time.
Revised:  This block-factorisation can provably be obtained in O%DIFDELCMD < \left(%%% N \log^{2 ( N \log} ( N ) %DIFDELCMD < \left( %%% \log^{d /\epsilon) + \log^{2 ( N ) }%DIFDELCMD < \right)%%% ^{4d+1 }%DIFDELCMD < \right) %%% complexity in time.
Edit intent: fluency
Original:  This block-factorisation can provably be obtained in O%DIFDELCMD < \left(%%% N \log^{2 ( N \log} ( N ) %DIFDELCMD < \left( %%% \log(1 /\epsilon) + \log^{2 ( N ) }%DIFDELCMD < \right)%%% ^{4d+1 }%DIFDELCMD < \right) %%% complexity in time.
Revised:  This block-factorisation can provably be obtained in O%DIFDELCMD < \left(%%% N \log^{2 ( N \log} ( N ) %DIFDELCMD < \left( %%% \log(1 /\epsilon) ( N ) }%DIFDELCMD < \right)%%% ^{4d+1 }%DIFDELCMD < \right) %%% complexity in time.
Edit intent: coherence
Original:  Numerical evidence further suggests that element-wise Cholesky decomposition with the same ordering constitutes an O%DIFDELCMD < \left( %%%  N \log^{2}( N ) \log^{2d}( N /\epsilon) %DIFDELCMD < \right) %%% solver .
Revised:  Numerical evidence further suggests that element-wise Cholesky decomposition with the same ordering constitutes an O%DIFDELCMD < \left( %%% N \log^{2}( N ) \log^{2d}( N /\epsilon) %DIFDELCMD < \right) %%% ) in time .
Edit intent: clarity
Original:  By inverting the order of the Cholesky decomposition we also obtain a near-linear-time solver for elliptic PDEs ( N \log( N ) \log^{d}( N /\epsilon) ) in space and \mathcal{O} ( N \log^{2}( N ) \log^{2d}( N /\epsilon) ) in time} .
Revised:  By inverting the order of the Cholesky decomposition we also obtain a solver for elliptic PDEs ( N \log( N ) \log^{d}( N /\epsilon) ) in space and \mathcal{O} ( N \log^{2}( N ) \log^{2d}( N /\epsilon) ) in time} .
Edit intent: clarity
Original:  For covariance functions that are Green's functions of elliptic boundary value problems and approximately equally spaced sampling points, we show how to identify a subset S \subset \{ 1 , \dots , N \} \times \{ 1 ,%DIFDELCMD < \dots %%% , N \ with \# S = \mathcal{O ( N \log (N) \log^{d} ( N /\epsilon ) ), such that the zero fill-in incomplete Cholesky factorisation of \Theta _{ i,j } \mathbb{1 _{( i, j ) \in S} is an \epsilon-approximation of \Theta.
Revised:  For covariance functions that are Green's functions of elliptic boundary value problems and homogeneously-distributed sampling points, we show how to identify a subset S \subset \{ 1 , \dots , N \} \times \{ 1 ,%DIFDELCMD < \dots %%% , N \ with \# S = \mathcal{O ( N \log (N) \log^{d} ( N /\epsilon ) ), such that the zero fill-in incomplete Cholesky factorisation of \Theta _{ i,j } \mathbb{1 _{( i, j ) \in S} is an \epsilon-approximation of \Theta.
Edit intent: clarity
Original:  For covariance functions that are Green's functions of elliptic boundary value problems and approximately equally spaced sampling points, we show how to identify a subset S \subset \{ 1 , \dots , N \} \times \{ 1 ,%DIFDELCMD < \dots %%% , N \ with \# S = \mathcal{O ( N \log (N) \log^{d} ( N /\epsilon ) ), such that the zero fill-in incomplete Cholesky factorisation of \Theta _{ i,j } \mathbb{1 _{( i, j ) \in S} is an \epsilon-approximation of \Theta.
Revised:  For covariance functions that are Green's functions of elliptic boundary value problems and approximately equally spaced sampling points, we show how to identify a subset S \subset \{ 1 , \dots , N \} %DIFDELCMD < \dots %%% , N \ with \# S = \mathcal{O ( N \log (N) \log^{d} ( N /\epsilon ) ), such that the zero fill-in incomplete Cholesky factorisation of \Theta _{ i,j } \mathbb{1 _{( i, j ) \in S} is an \epsilon-approximation of \Theta.
Edit intent: coherence
Original:  For covariance functions that are Green's functions of elliptic boundary value problems and approximately equally spaced sampling points, we show how to identify a subset S \subset \{ 1 , \dots , N \} \times \{ 1 ,%DIFDELCMD < \dots %%% , N \ with \# S = \mathcal{O ( N \log (N) \log^{d} ( N /\epsilon ) ), such that the zero fill-in incomplete Cholesky factorisation of \Theta _{ i,j } \mathbb{1 _{( i, j ) \in S} is an \epsilon-approximation of \Theta.
Revised:  For covariance functions that are Green's functions of elliptic boundary value problems and approximately equally spaced sampling points, we show how to identify a subset S \subset \{ 1 , \dots , N \} \times \{ 1 ,%DIFDELCMD < \dots %%% , N \ with \# S = O ( N \log (N) \log^{d} ( N /\epsilon ) ), such that the zero fill-in incomplete Cholesky factorisation of \Theta _{ i,j } \mathbb{1 _{( i, j ) \in S} is an \epsilon-approximation of \Theta.
Edit intent: clarity
Original:  For covariance functions that are Green's functions of elliptic boundary value problems and approximately equally spaced sampling points, we show how to identify a subset S \subset \{ 1 , \dots , N \} \times \{ 1 ,%DIFDELCMD < \dots %%% , N \ with \# S = \mathcal{O ( N \log (N) \log^{d} ( N /\epsilon ) ), such that the zero fill-in incomplete Cholesky factorisation of \Theta _{ i,j } \mathbb{1 _{( i, j ) \in S} is an \epsilon-approximation of \Theta.
Revised:  For covariance functions that are Green's functions of elliptic boundary value problems and approximately equally spaced sampling points, we show how to identify a subset S \subset \{ 1 , \dots , N \} \times \{ 1 ,%DIFDELCMD < \dots %%% , N \ with \# S = \mathcal{O ( N \log (N) \log^{d} ( N /\epsilon ) ), such that the zero fill-in incomplete Cholesky factorisation of the sparse matrix \Theta _{ i,j } \mathbb{1 _{( i, j ) \in S} is an \epsilon-approximation of \Theta.
Edit intent: clarity
Original:  For covariance functions that are Green's functions of elliptic boundary value problems and approximately equally spaced sampling points, we show how to identify a subset S \subset \{ 1 , \dots , N \} \times \{ 1 ,%DIFDELCMD < \dots %%% , N \ with \# S = \mathcal{O ( N \log (N) \log^{d} ( N /\epsilon ) ), such that the zero fill-in incomplete Cholesky factorisation of \Theta _{ i,j } \mathbb{1 _{( i, j ) \in S} is an \epsilon-approximation of \Theta.
Revised:  For covariance functions that are Green's functions of elliptic boundary value problems and approximately equally spaced sampling points, we show how to identify a subset S \subset \{ 1 , \dots , N \} \times \{ 1 ,%DIFDELCMD < \dots %%% , N \ with \# S = \mathcal{O ( N \log (N) \log^{d} ( N /\epsilon ) ), such that the zero fill-in incomplete Cholesky factorisation of \Theta _{ ij } \mathbb{1 _{( i, j ) \in S} is an \epsilon-approximation of \Theta.
Edit intent: fluency
Original:  For covariance functions that are Green's functions of elliptic boundary value problems and approximately equally spaced sampling points, we show how to identify a subset S \subset \{ 1 , \dots , N \} \times \{ 1 ,%DIFDELCMD < \dots %%% , N \ with \# S = \mathcal{O ( N \log (N) \log^{d} ( N /\epsilon ) ), such that the zero fill-in incomplete Cholesky factorisation of \Theta _{ i,j } \mathbb{1 _{( i, j ) \in S} is an \epsilon-approximation of \Theta.
Revised:  For covariance functions that are Green's functions of elliptic boundary value problems and approximately equally spaced sampling points, we show how to identify a subset S \subset \{ 1 , \dots , N \} \times \{ 1 ,%DIFDELCMD < \dots %%% , N \ with \# S = \mathcal{O ( N \log (N) \log^{d} ( N /\epsilon ) ), such that the zero fill-in incomplete Cholesky factorisation of \Theta _{ i,j } 1 _{( i, j ) \in S} is an \epsilon-approximation of \Theta.
Edit intent: clarity
Original:  This block-factorisation can provably be obtained in complexity \mathcal{O ( N \log( N ) \log^{d}( N /\epsilon) ) in space and \mathcal{O ( N \log^{2}( N ) \log^{2d}( N /\epsilon) ) in time  .
Revised:  This block-factorisation can provably be obtained in complexity O ( N \log( N ) \log^{d}( N /\epsilon) ) in space and \mathcal{O ( N \log^{2}( N ) \log^{2d}( N /\epsilon) ) in time .
Edit intent: fluency
Original:  This block-factorisation can provably be obtained in complexity \mathcal{O ( N \log( N ) \log^{d}( N /\epsilon) ) in space and \mathcal{O ( N \log^{2}( N ) \log^{2d}( N /\epsilon) ) in time  .
Revised:  This block-factorisation can provably be obtained in complexity \mathcal{O ( N \log( N ) \log^{d}( N /\epsilon) ) in space and O ( N \log^{2}( N ) \log^{2d}( N /\epsilon) ) in time .
Edit intent: fluency
Original:  The algorithm only needs to know the spatial configuration of the x_{i} and does not require an analytic representation of G. Furthermore, an approximate PCA with optimal rate of convergence in the operator norm can be easily read off from this decomposition .
Revised:  The algorithm only needs to know the spatial configuration of the x_{i} and does not require an analytic representation of G. Furthermore, an approximate PCA with optimal rate of convergence in the operator norm .
Edit intent: clarity
Original:  Hence, by using only subsampling and the incomplete Cholesky decomposition , we obtain  at nearly linear complexity  the compression, inversion and approximate PCA of a large class of covariance matrices.
Revised:  Hence, by using only subsampling and the incomplete Cholesky decomposition , we obtain , at nearly linear complexity the compression, inversion and approximate PCA of a large class of covariance matrices.
Edit intent: fluency