wanyu/IteraTeR_v2 huggingface dataset:
Original:  Moreover, above a critical field amplitudemorphogenesis exhibits reversal dynamics: a fully developed animal folds back into its incipient spheroid morphology.
Revised:  Moreover, above a critical field amplitudemorphogenesis exhibits reversal dynamics: a fully developed Hydra folds back into its incipient spheroid morphology.
Edit intent: clarity
Original:  Reversal of morphogenesis is shown to be triggered by enhanced electrical excitations in the Hydra tissue, leading to intensified calcium activity .
Revised:  Reversal of morphogenesis is shown to be triggered by enhanced epithelial electrical excitations, accompanied by intensified calcium activity .
Edit intent: clarity
Original:  These results indicate that electrical processes are tightly integrated with biochemical and mechanical processes in morphogenesis, and play an instructive role to a level that can direct developmental trajectories.
Revised:  These results indicate that electrical processes play an instructive role to a level that can direct developmental trajectories.
Edit intent: clarity
Original:  The capability to reverse the dynamics of morphogenesis and tune its course by an external control , calls for extending the study of development beyond forward-driven  hierarchical processes.
Revised:  Reversal of morphogenesis by external fields , calls for extending the study of development beyond forward-driven hierarchical processes.
Edit intent: clarity
Original:  The capability to reverse the dynamics of morphogenesis and tune its course by an external control , calls for extending the study of development beyond forward-driven  hierarchical processes.
Revised:  The capability to reverse the dynamics of morphogenesis and tune its course by an external control , calls for extending its framework beyond programmatic, forward-driven hierarchical processes.
Edit intent: clarity
Original:  The capability to reverse the dynamics of morphogenesis and tune its course by an external control , calls for extending the study of development beyond forward-driven  hierarchical processes.
Revised:  The capability to reverse the dynamics of morphogenesis and tune its course by an external control , calls for extending the study of development beyond forward-driven , hierarchical processes.
Edit intent: fluency
Original: For non-convex optimization in machine learning, this paper proves that every local minimum achieves the global optimality of the perturbable gradient basis model at any differentiable point.
Revised: For non-convex optimization in machine learning, this paper proves that every local minimum achieves the globally optimal value of the perturbable gradient basis model at any differentiable point.
Edit intent: clarity
Original: For non-convex optimization in machine learning, this paper proves that every local minimum achieves the globally optimal value of the perturbable gradient basis model at any differentiable point.
Revised: For nonconvex optimization in machine learning, this paper proves that every local minimum achieves the globally optimal value of the perturbable gradient basis model at any differentiable point.
Edit intent: fluency
Original: For non-convex optimization in machine learning, this paper proves that every local minimum achieves the globally optimal value of the perturbable gradient basis model at any differentiable point.
Revised: For non-convex optimization in machine learning, this article proves that every local minimum achieves the globally optimal value of the perturbable gradient basis model at any differentiable point.
Edit intent: fluency
Original:  As a result, non-convex machine learning is theoretically as supported as convex machine learning with a hand-crafted basis in terms of the loss at differentiable local minima, except in the case when a preference is given to the hand-crafted basis over the perturbable gradient basis.
Revised:  As a result, nonconvex machine learning is theoretically as supported as convex machine learning with a hand-crafted basis in terms of the loss at differentiable local minima, except in the case when a preference is given to the hand-crafted basis over the perturbable gradient basis.
Edit intent: fluency
Original:  As a result, non-convex machine learning is theoretically as supported as convex machine learning with a hand-crafted basis in terms of the loss at differentiable local minima, except in the case when a preference is given to the hand-crafted basis over the perturbable gradient basis.
Revised:  As a result, non-convex machine learning is theoretically as supported as convex machine learning with a handcrafted basis in terms of the loss at differentiable local minima, except in the case when a preference is given to the hand-crafted basis over the perturbable gradient basis.
Edit intent: fluency
Original:  As a result, non-convex machine learning is theoretically as supported as convex machine learning with a hand-crafted basis in terms of the loss at differentiable local minima, except in the case when a preference is given to the hand-crafted basis over the perturbable gradient basis.
Revised:  As a result, non-convex machine learning is theoretically as supported as convex machine learning with a hand-crafted basis in terms of the loss at differentiable local minima, except in the case when a preference is given to the handcrafted basis over the perturbable gradient basis.
Edit intent: fluency
Original:  Furthermore, as special cases of our general results, this paper improves or complements several state-of-the-art theoretical results on deep neural networks, deep residual networks, and over-parameterized deep neural networks with a unified proof technique and novel geometric insights.
Revised:  Furthermore, as special cases of our general results, this article improves or complements several state-of-the-art theoretical results on deep neural networks, deep residual networks, and over-parameterized deep neural networks with a unified proof technique and novel geometric insights.
Edit intent: fluency
Original:  Furthermore, as special cases of our general results, this paper improves or complements several state-of-the-art theoretical results on deep neural networks, deep residual networks, and over-parameterized deep neural networks with a unified proof technique and novel geometric insights.
Revised:  Furthermore, as special cases of our general results, this paper improves or complements several state-of-the-art theoretical results on deep neural networks, deep residual networks, and overparameterized deep neural networks with a unified proof technique and novel geometric insights.
Edit intent: fluency
Original:  A special case of our results  contributes to the theoretical foundation of representation learning .
Revised:  A special case of our results also contributes to the theoretical foundation of representation learning .
Edit intent: clarity
Original:  Further , we achieve the first sub-linear time  approximation algorithm for  MEB with outliers .
Revised:  Further , we achieve the first sub-linear time approximation algorithm for the MEB with outliers .
Edit intent: fluency
Original:  We expect that our technique will be applicable to design sub-linear time algorithms for other shape fitting with outliers problems.
Revised:  We expect that our technique will be applicable to design sub-linear time algorithms for other optimization problems.
Edit intent: clarity
Original:  The well-known swap algorithm would be inefficient when the size of the matrix becomes large or when the matrix is too sparse/ full .
Revised:  The well-known swap algorithm would be inefficient when the size of the matrix becomes large or when the matrix is too sparse/ dense .
Edit intent: clarity
Original:  Here we propose the Rectangle loop algorithm, a Markov-chain Monte Carlo algorithm to sample binary matrices with fixed margins uniformly.
Revised:  Here we propose the Rectangle Loop algorithm, a Markov-chain Monte Carlo algorithm to sample binary matrices with fixed margins uniformly.
Edit intent: fluency
Original:  Here we propose the Rectangle loop algorithm, a Markov-chain Monte Carlo algorithm to sample binary matrices with fixed margins uniformly.
Revised:  Here we propose the Rectangle loop algorithm, a Markov chain Monte Carlo algorithm to sample binary matrices with fixed margins uniformly.
Edit intent: fluency
Original:  Theoretically the Rectangle loop algorithm is better than the swap algorithm in Peskun's order.
Revised:  Theoretically the Rectangle Loop algorithm is better than the swap algorithm in Peskun's order.
Edit intent: fluency
Original:  Empirically studies also demonstrates the Rectangle loop algorithm is remarkablely more efficient than the swap algorithm.
Revised:  Empirically studies also demonstrates the Rectangle Loop algorithm is remarkablely more efficient than the swap algorithm.
Edit intent: fluency
Original: For the tensor PCA (principal component analysis) problem, we propose a new hierarchy of algorithms that are increasingly powerful yet require increasing runtime.
Revised: For the tensor PCA (principal component analysis) problem, we propose a new hierarchy of increasingly powerful algorithms with increasing runtime.
Edit intent: clarity
Original:  Our level-\ell algorithm can be thought of as a (linearized ) message-passing algorithm that keeps track of \ell-wise dependencies among the hidden variables.
Revised:  Our level-\ell algorithm can be thought of as a linearized message-passing algorithm that keeps track of \ell-wise dependencies among the hidden variables.
Edit intent: fluency
Original:  Specifically, our algorithms are spectral methods based on the Kikuchi Hessian matrix , which generalizes the well-studied Bethe Hessian matrix to the higher-order Kikuchi free energies.
Revised:  Specifically, our algorithms are spectral methods based on the Kikuchi Hessian , which generalizes the well-studied Bethe Hessian matrix to the higher-order Kikuchi free energies.
Edit intent: fluency
Original:  Specifically, our algorithms are spectral methods based on the Kikuchi Hessian matrix , which generalizes the well-studied Bethe Hessian matrix to the higher-order Kikuchi free energies.
Revised:  Specifically, our algorithms are spectral methods based on the Kikuchi Hessian matrix , which generalizes the well-studied Bethe Hessian to the higher-order Kikuchi free energies.
Edit intent: fluency
Original:  In this work we ` redeem' the statistical physics approach by showing that our hierarchy gives a polynomial-time algorithm matching the performance of SOS.
Revised:  In this work we ' redeem' the statistical physics approach by showing that our hierarchy gives a polynomial-time algorithm matching the performance of SOS.
Edit intent: fluency
Original: Stable matching in a community consisting of N men and N women is a classical combinatorial problem that has been the subject of intense theoretical and empirical study since its introduction in 1962 in a seminal paper by Gale and Shapley GS62 . In this paper, we study the number of stable pairs, that is, the man/woman pairs that appear in some stable matching.
Revised: Stable matching in a community consisting of N men and N women is a classical combinatorial problem that has been the subject of intense theoretical and empirical study since its introduction in 1962 in a seminal paper by Gale and Shapley . In this paper, we study the number of stable pairs, that is, the man/woman pairs that appear in some stable matching.
Edit intent: coherence
Original:  We prove that if the preference lists on one side are generated at random using the popularity model of Immorlica and Mahdian IM15 , the expected number of stable edges is bounded by N  + N ln N , matching the asymptotic bound for uniform preference lists.
Revised:  We prove that if the preference lists on one side are generated at random using the popularity model of Immorlica and Mahdian IM15 , the expected number of stable edges is bounded by N + N ln N , matching the asymptotic value for uniform preference lists.
Edit intent: clarity
Original: Stable matching in a community consisting of N men and N women is a classical combinatorial problem that has been the subject of intense theoretical and empirical study since its introduction in 1962 in a seminal paper by Gale and Shapley .
Revised: Stable matching in a community consisting of men and women is a classical combinatorial problem that has been the subject of intense theoretical and empirical study since its introduction in 1962 in a seminal paper by Gale and Shapley .
Edit intent: clarity
Original:  In this paper, we propose a nucleus neural network (NNN) and corresponding architecture and parameter learning methods .
Revised:  In this paper, we propose a nucleus neural network (NNN) and corresponding connecting architecture learning method .
Edit intent: clarity
Original:  This  architecture gets rid of layer limitation and may lead to more powerful learning capability.
Revised:  This type of architecture gets rid of layer limitation and may lead to more powerful learning capability.
Edit intent: clarity
Original:  Based on the principle that more relevant input and output neuron pair deserves higher connecting density, we propose an  architecture learning model for the nucleus.
Revised:  Based on the principle that more relevant input and output neuron pair deserves higher connecting density, we propose an efficient architecture learning model for the nucleus.
Edit intent: clarity
Original:  Moreover, we propose an improved learning method for learning connecting weights and biases with the optimized architecture.
Revised:  Moreover, we improve the learning method for learning connecting weights and biases with the optimized architecture.
Edit intent: clarity
Original:  Moreover, we propose an improved learning method for learning connecting weights and biases with the optimized architecture.
Revised:  Moreover, we propose an improved learning method for connecting weights and biases with the optimized architecture.
Edit intent: fluency
Original:  Moreover, we propose an improved learning method for learning connecting weights and biases with the optimized architecture.
Revised:  Moreover, we propose an improved learning method for learning connecting weights and biases given the optimized architecture.
Edit intent: clarity
Original:  So we define a super robust learning problem and test the proposed network with one case where the types of image backgrounds in training and test sets are different.
Revised:  So we define a super robust learning problem and test the proposed network with one case where the types of digital backgrounds in training and test sets are different.
Edit intent: clarity
Original:  (where%DIFDELCMD < {\bf %%% x \in \mathbb{R of the initial-value problem for the transient 2D scalar wave equation at t>0 through the initial conditions for both u and v=\partial u/\partial t . For the purpose of constructing a two-step time-marching algorithm, an additional integral representation formula for the sum u(%DIFDELCMD < {\bf %%% x ,t_*+\tau)+ u(%DIFDELCMD < {\bf %DIFDELCMD < %%% x ,t_*-\tau) is provided, with \tau being a time step and t_*%DIFDELCMD < \ge %%% \tau .
Revised:  (where%DIFDELCMD < {\bf %%% \in \mathbb{R of the initial-value problem for the transient 2D scalar wave equation at t>0 through the initial conditions for both u and v=\partial u/\partial t . For the purpose of constructing a two-step time-marching algorithm, an additional integral representation formula for the sum u(%DIFDELCMD < {\bf %%% x ,t_*+\tau)+ u(%DIFDELCMD < {\bf %DIFDELCMD < %%% x ,t_*-\tau) is provided, with \tau being a time step and t_*%DIFDELCMD < \ge %%% \tau .
Edit intent: fluency
Original:  (where%DIFDELCMD < {\bf %%% x \in \mathbb{R of the initial-value problem for the transient 2D scalar wave equation at t>0 through the initial conditions for both u and v=\partial u/\partial t . For the purpose of constructing a two-step time-marching algorithm, an additional integral representation formula for the sum u(%DIFDELCMD < {\bf %%% x ,t_*+\tau)+ u(%DIFDELCMD < {\bf %DIFDELCMD < %%% x ,t_*-\tau) is provided, with \tau being a time step and t_*%DIFDELCMD < \ge %%% \tau .
Revised:  (where%DIFDELCMD < {\bf %%% x of the initial-value problem for the transient 2D scalar wave equation at t>0 through the initial conditions for both u and v=\partial u/\partial t . For the purpose of constructing a two-step time-marching algorithm, an additional integral representation formula for the sum u(%DIFDELCMD < {\bf %%% x ,t_*+\tau)+ u(%DIFDELCMD < {\bf %DIFDELCMD < %%% x ,t_*-\tau) is provided, with \tau being a time step and t_*%DIFDELCMD < \ge %%% \tau .
Edit intent: clarity
Original:  (where%DIFDELCMD < {\bf %%% x \in \mathbb{R of the initial-value problem for the transient 2D scalar wave equation at t>0 through the initial conditions for both u and v=\partial u/\partial t . For the purpose of constructing a two-step time-marching algorithm, an additional integral representation formula for the sum u(%DIFDELCMD < {\bf %%% x ,t_*+\tau)+ u(%DIFDELCMD < {\bf %DIFDELCMD < %%% x ,t_*-\tau) is provided, with \tau being a time step and t_*%DIFDELCMD < \ge %%% \tau .
Revised:  (where%DIFDELCMD < {\bf %%% x \in \mathbb{R of the initial-value problem for the transient 2D scalar wave equation at any time point through the initial conditions for both u and v=\partial u/\partial t . For the purpose of constructing a two-step time-marching algorithm, an additional integral representation formula for the sum u(%DIFDELCMD < {\bf %%% x ,t_*+\tau)+ u(%DIFDELCMD < {\bf %DIFDELCMD < %%% x ,t_*-\tau) is provided, with \tau being a time step and t_*%DIFDELCMD < \ge %%% \tau .
Edit intent: clarity
Original:  (where%DIFDELCMD < {\bf %%% x \in \mathbb{R of the initial-value problem for the transient 2D scalar wave equation at t>0 through the initial conditions for both u and v=\partial u/\partial t . For the purpose of constructing a two-step time-marching algorithm, an additional integral representation formula for the sum u(%DIFDELCMD < {\bf %%% x ,t_*+\tau)+ u(%DIFDELCMD < {\bf %DIFDELCMD < %%% x ,t_*-\tau) is provided, with \tau being a time step and t_*%DIFDELCMD < \ge %%% \tau .
Revised:  (where%DIFDELCMD < {\bf %%% x \in \mathbb{R of the initial-value problem for the transient 2D scalar wave equation at t>0 through the initial conditions . For the purpose of constructing a two-step time-marching algorithm, an additional integral representation formula for the sum u(%DIFDELCMD < {\bf %%% x ,t_*+\tau)+ u(%DIFDELCMD < {\bf %DIFDELCMD < %%% x ,t_*-\tau) is provided, with \tau being a time step and t_*%DIFDELCMD < \ge %%% \tau .
Edit intent: coherence
Original:  (where%DIFDELCMD < {\bf %%% x \in \mathbb{R of the initial-value problem for the transient 2D scalar wave equation at t>0 through the initial conditions for both u and v=\partial u/\partial t . For the purpose of constructing a two-step time-marching algorithm, an additional integral representation formula for the sum u(%DIFDELCMD < {\bf %%% x ,t_*+\tau)+ u(%DIFDELCMD < {\bf %DIFDELCMD < %%% x ,t_*-\tau) is provided, with \tau being a time step and t_*%DIFDELCMD < \ge %%% \tau .
Revised:  (where%DIFDELCMD < {\bf %%% x \in \mathbb{R of the initial-value problem for the transient 2D scalar wave equation at t>0 through the initial conditions for both u and v=\partial u/\partial t . For the purpose of constructing a two-step time-marching algorithm, an additional integral representation formula %DIFDELCMD < {\bf %%% x ,t_*+\tau)+ u(%DIFDELCMD < {\bf %DIFDELCMD < %%% x ,t_*-\tau) is provided, with \tau being a time step and t_*%DIFDELCMD < \ge %%% \tau .
Edit intent: clarity
Original:  (where%DIFDELCMD < {\bf %%% x \in \mathbb{R of the initial-value problem for the transient 2D scalar wave equation at t>0 through the initial conditions for both u and v=\partial u/\partial t . For the purpose of constructing a two-step time-marching algorithm, an additional integral representation formula for the sum u(%DIFDELCMD < {\bf %%% x ,t_*+\tau)+ u(%DIFDELCMD < {\bf %DIFDELCMD < %%% x ,t_*-\tau) is provided, with \tau being a time step and t_*%DIFDELCMD < \ge %%% \tau .
Revised:  (where%DIFDELCMD < {\bf %%% x \in \mathbb{R of the initial-value problem for the transient 2D scalar wave equation at t>0 through the initial conditions for both u and v=\partial u/\partial t . For the purpose of constructing a two-step time-marching algorithm, an additional integral representation formula for the sum u(%DIFDELCMD < {\bf %%% ,t_*+\tau)+ u(%DIFDELCMD < {\bf %DIFDELCMD < %%% x ,t_*-\tau) is provided, with \tau being a time step and t_*%DIFDELCMD < \ge %%% \tau .
Edit intent: fluency
Original:  (where%DIFDELCMD < {\bf %%% x \in \mathbb{R of the initial-value problem for the transient 2D scalar wave equation at t>0 through the initial conditions for both u and v=\partial u/\partial t . For the purpose of constructing a two-step time-marching algorithm, an additional integral representation formula for the sum u(%DIFDELCMD < {\bf %%% x ,t_*+\tau)+ u(%DIFDELCMD < {\bf %DIFDELCMD < %%% x ,t_*-\tau) is provided, with \tau being a time step and t_*%DIFDELCMD < \ge %%% \tau .
Revised:  (where%DIFDELCMD < {\bf %%% x \in \mathbb{R of the initial-value problem for the transient 2D scalar wave equation at t>0 through the initial conditions for both u and v=\partial u/\partial t . For the purpose of constructing a two-step time-marching algorithm, an additional integral representation formula for the sum u(%DIFDELCMD < {\bf %%% x ,t_*+\tau)+ u(%DIFDELCMD < {\bf %DIFDELCMD < %%% ,t_*-\tau) is provided, with \tau being a time step and t_*%DIFDELCMD < \ge %%% \tau .
Edit intent: fluency
Original:  It is shown that integrals in the two representation formulas are easily calculated if the initial conditions and u(%DIFDELCMD < {\bf %%% x ,t_*) as functions of spatial coordinates are approximated by stencil interpolation polynomials in the neighborhood of any point %DIFDELCMD < {\bf %%% x _{ij in a 2D Cartesian grid \{(ih,jh),(i,j) \in \mathbb{Z^2\} where h is a grid spacing} .
Revised:  It is shown that integrals in the two representation formulas are easily calculated if the initial conditions and %DIFDELCMD < {\bf %%% x ,t_*) as functions of spatial coordinates are approximated by stencil interpolation polynomials in the neighborhood of any point %DIFDELCMD < {\bf %%% x _{ij in a 2D Cartesian grid \{(ih,jh),(i,j) \in \mathbb{Z^2\} where h is a grid spacing} .
Edit intent: clarity
Original:  It is shown that integrals in the two representation formulas are easily calculated if the initial conditions and u(%DIFDELCMD < {\bf %%% x ,t_*) as functions of spatial coordinates are approximated by stencil interpolation polynomials in the neighborhood of any point %DIFDELCMD < {\bf %%% x _{ij in a 2D Cartesian grid \{(ih,jh),(i,j) \in \mathbb{Z^2\} where h is a grid spacing} .
Revised:  It is shown that integrals in the two representation formulas are easily calculated if the initial conditions and u(%DIFDELCMD < {\bf %%% ,t_*) as functions of spatial coordinates are approximated by stencil interpolation polynomials in the neighborhood of any point %DIFDELCMD < {\bf %%% x _{ij in a 2D Cartesian grid \{(ih,jh),(i,j) \in \mathbb{Z^2\} where h is a grid spacing} .
Edit intent: fluency
Original:  It is shown that integrals in the two representation formulas are easily calculated if the initial conditions and u(%DIFDELCMD < {\bf %%% x ,t_*) as functions of spatial coordinates are approximated by stencil interpolation polynomials in the neighborhood of any point %DIFDELCMD < {\bf %%% x _{ij in a 2D Cartesian grid \{(ih,jh),(i,j) \in \mathbb{Z^2\} where h is a grid spacing} .
Revised:  It is shown that integrals in the two representation formulas are easily calculated if the initial conditions and u(%DIFDELCMD < {\bf %%% x ,t_*) as functions of spatial coordinates are approximated by stencil interpolation polynomials in the neighborhood of any point %DIFDELCMD < {\bf %%% _{ij in a 2D Cartesian grid \{(ih,jh),(i,j) \in \mathbb{Z^2\} where h is a grid spacing} .
Edit intent: fluency