wanyu/IteraTeR_v2 huggingface dataset:
Original:  Here h^\star is the maximum size of a graph in }{\cal   [ STOC 2010 ] . In this paper we turn the wheel back, and design an alternate algorithm for TMC by giving a direct reduction to a version of unique linkage theorem appearing in Graph Minors XXII of Robertson and Seymour.
Revised:  Here h^\star is the maximum size of a graph in }{\cal F [ STOC 2010 ] . In this paper we turn the wheel back, and design an alternate algorithm for TMC by giving a direct reduction to a version of unique linkage theorem appearing in Graph Minors XXII of Robertson and Seymour.
Edit intent: fluency
Original:  While most works in the literature rely on a degree of sparsity to provide guarantees of consistent graph recovery , our analysis moves away from this condition and includes the demanding setting of dense connectivity .
Revised:  The main question is to establish technical guarantees of consistent graph recovery , our analysis moves away from this condition and includes the demanding setting of dense connectivity .
Edit intent: clarity
Original:  This claim is proved for three matrix estimators: i) the Granger estimator that adapts to the partial observability setting the solution that is optimal under full observability ;
Revised:  This claim is proved for three matrix estimators: i) the Granger estimator that adapts to the partial observability setting the solution that is exact under full observability ;
Edit intent: clarity
Original:   Comparison among the estimators is performed through illustrative examples that reveal how estimators that are not optimal in the full observability regime can outperform the Granger estimator in the partial observability regime.
Revised:  Comparison among the estimators is performed through illustrative examples that show how estimators that are not optimal in the full observability regime can outperform the Granger estimator in the partial observability regime.
Edit intent: clarity
Original:  The analysis reveals that the fundamental property enabling consistent graph learning is the statistical concentration of node degrees , rather than the sparsity of connections .
Revised:  The analysis reveals that the fundamental property enabling consistent graph learning is the statistical concentration of node degrees .
Edit intent: clarity
Original:  In this paper we present and implement an adaptation of the octilinear mixed-integer linear programming approach of N\"ollenburg and Wolff (2011) that can draw k-linear metro maps .
Revised:  In this paper we present and implement an adaptation of the octolinear mixed-integer linear programming approach of N\"ollenburg and Wolff (2011) that can draw k-linear metro maps .
Edit intent: fluency
Original: We propose an analytically tractable class of models for the dynamics of a limit order book, described as the solution of a stochastic partial differential equation (SPDE) with multiplicative noise  .
Revised: We propose an analytically tractable class of models for the dynamics of a limit order book, described through a stochastic partial differential equation (SPDE) with multiplicative noise .
Edit intent: clarity
Original:  We provide conditions under which the model admits a finite dimensional realization driven by a (low-dimensional) Markov process, leading to efficient methods for estimation and computation  .
Revised:  We provide conditions under which the model admits a finite dimensional realization driven by a (low-dimensional) Markov process, leading to efficient estimation and computation .
Edit intent: clarity
Original:  We provide conditions under which the model admits a finite dimensional realization driven by a (low-dimensional) Markov process, leading to efficient methods for estimation and computation  .
Revised:  We provide conditions under which the model admits a finite dimensional realization driven by a (low-dimensional) Markov process, leading to efficient methods for estimation and computation methods .
Edit intent: clarity
Original:  We study two examples of parsimonious models in this class: a two-factor model and a model in which the order book depth is mean-reverting .
Revised:  We study two examples of parsimonious models in this class: a two-factor model and a model with mean-reverting order book depth is mean-reverting .
Edit intent: clarity
Original:  We study two examples of parsimonious models in this class: a two-factor model and a model in which the order book depth is mean-reverting .
Revised:  We study two examples of parsimonious models in this class: a two-factor model and a model in which the order book depth .
Edit intent: clarity
Original:  We improve this result to \tilde O(\min\{q,n^2\}{\varepsilon^2}) , matching a lower bound of Kolmogorov (2018) up to logarithmic factors .
Revised:  We improve this to \tilde O(\min\{q,n^2\}{\varepsilon^2}) , matching a lower bound of Kolmogorov (2018) up to logarithmic factors .
Edit intent: clarity
Original:  This is improved to roughly \tilde O( \frac{1/\mu_{\ast}+\min\{q + n,n^2\}}{\varepsilon^2}) for applications in which the coefficients are known to be log-concave (e.g.\ for connected subgraphs of a given graph).
Revised:  This is improved to roughly \tilde O( \frac{1/\mu_{\ast}+\min\{q + n,n^2\}}{\varepsilon^2}) for applications where the coefficients are known to be log-concave (e.g.\ for connected subgraphs of a given graph).
Edit intent: clarity
Original:  This is improved to roughly \tilde O( \frac{1/\mu_{\ast}+\min\{q + n,n^2\}}{\varepsilon^2}) for applications in which the coefficients are known to be log-concave (e.g.\ for connected subgraphs of a given graph).
Revised:  This is improved to roughly \tilde O( \frac{1/\mu_{\ast}+\min\{q + n,n^2\}}{\varepsilon^2}) for applications in which the coefficients are log-concave (e.g.\ for connected subgraphs of a given graph).
Edit intent: clarity
Original:  After deriving basic properties of average sensitivity such as composability , we provide efficient approximation algorithms with low average sensitivities for concrete graph problems, including the minimum spanning forest problem, the global minimum cut problem, the  maximum matching problem , and the minimum vertex cover problem .
Revised:  After deriving basic properties of average sensitivity such as composition , we provide efficient approximation algorithms with low average sensitivities for concrete graph problems, including the minimum spanning forest problem, the global minimum cut problem, the maximum matching problem , and the minimum vertex cover problem .
Edit intent: clarity
Original:  After deriving basic properties of average sensitivity such as composition, we provide efficient approximation algorithms with low average sensitivities for concrete graph problems, including the minimum spanning forest problem, the global minimum cut problem, the s-t minimum cut problem, the balanced cut problem, and the maximum matching problem.
Revised:  After deriving basic properties of average sensitivity such as composition, we provide efficient approximation algorithms with low average sensitivities for concrete graph problems, including the minimum spanning forest problem, the global minimum cut problem, the minimum s-t cut problem, the balanced cut problem, and the maximum matching problem.
Edit intent: fluency
Original:  After deriving basic properties of average sensitivity such as composition, we provide efficient approximation algorithms with low average sensitivities for concrete graph problems, including the minimum spanning forest problem, the global minimum cut problem, the s-t minimum cut problem, the balanced cut problem, and the maximum matching problem.
Revised:  After deriving basic properties of average sensitivity such as composition, we provide efficient approximation algorithms with low average sensitivities for concrete graph problems, including the minimum spanning forest problem, the global minimum cut problem, the s-t minimum cut problem, and the maximum matching problem.
Edit intent: clarity
Original:  The utility of the manifold-based surface construction techniques in isogeometric analysis was first demonstrated in Majeed and Cirak (CMAME, 2017).
Revised:  The utility of the manifold-based surface construction techniques in isogeometric analysis was demonstrated in Majeed and Cirak (CMAME, 2017).
Edit intent: coherence
Original:  The necessary smooth partition of unity, or blending, functions for the charts are assembled from tensor-product B-spline pieces and require in contrast to the construction in Majeed et al. no normalisation.
Revised:  The necessary smooth partition of unity, or blending, functions for the charts are assembled from tensor-product B-spline pieces and require in contrast to earlier constructions no normalisation.
Edit intent: clarity
Original:  Planar chart domains that include creased edges or are adjacent to the domain boundary require special local polynomial approximants in the partition of unity method .
Revised:  Planar chart domains that include creased edges or are adjacent to the domain boundary require special local polynomial approximants .
Edit intent: clarity
Original:  The new chart domain geometries are chosen so that it becomes trivial to establish the local polynomial approximants that are always C^0 continuous across the tagged edges.
Revised:  The new chart domain geometries are chosen so that it becomes trivial to establish local polynomial approximants that are always C^0 continuous across the tagged edges.
Edit intent: clarity
Original:  The new chart domain geometries are chosen so that it becomes trivial to establish the local polynomial approximants that are always C^0 continuous across the tagged edges.
Revised:  The new chart domain geometries are chosen so that it becomes trivial to establish the local polynomial approximants that are always C^0 continuous across tagged edges.
Edit intent: fluency
Original:  A large body of theoretical work has established sharp thresholds for weak and exact recovery, and sharp characterizations of the optimal reconstruction accuracy in such models, focusing however on the special case of Erd\"os-R\'enyi-type random graphs.
Revised:  A large body of theoretical work has established sharp thresholds for weak and exact recovery, and sharp characterizations of the optimal reconstruction accuracy in such models, focusing however on the special case of Erd\"os--R\'enyi-type random graphs.
Edit intent: fluency
Original:  We prove that the picture is dramatically different for graph sequences converging to transitive amenable graphs (including, for instance, d-dimensional grids).
Revised:  We prove that the picture is dramatically different for graph sequences converging to amenable graphs (including, for instance, d-dimensional grids).
Edit intent: clarity
Original:  We consider a model in which an arbitrarily small fraction of the vertex labels is revealed to the algorithm , and show that a linear-time  algorithm can achieve reconstruction accuracy that is arbitrarily close to the information-theoretic optimum.
Revised:  We consider a model in which an arbitrarily small fraction of the vertex labels is revealed , and show that a linear-time algorithm can achieve reconstruction accuracy that is arbitrarily close to the information-theoretic optimum.
Edit intent: clarity
Original:  Indeed, focusing on group synchronization on random regular graphs, we prove that the information-computation gap persists if a small amounts of additional side information revealed about the labels \theta_i's .
Revised:  Indeed, focusing on group synchronization on random regular graphs, we prove that the information-computation gap still persists even when a small amount of side information is revealed .
Edit intent: clarity
Original: We present data structures and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations.
Revised: We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations.
Edit intent: clarity
Original:  We formulate this problem precisely and boil it down to goodness of fit testing for graph-valued, infinite-state Markov processes and exhibit and analyze a  test based on a procedure that we call non-stationary sampling for a natural class of models.
Revised:  We formulate this problem precisely and boil it down to goodness of fit testing for graph-valued, infinite-state Markov processes and exhibit and analyze a universal test based on a procedure that we call non-stationary sampling for a natural class of models.
Edit intent: clarity
Original:  We formulate this problem precisely and boil it down to goodness of fit testing for graph-valued, infinite-state Markov processes and exhibit and analyze a  test based on a procedure that we call non-stationary sampling for a natural class of models.
Revised:  We formulate this problem precisely and boil it down to goodness of fit testing for graph-valued, infinite-state Markov processes and exhibit and analyze a test based on non-stationary sampling for a natural class of models.
Edit intent: clarity
Original:  The experiments indicate that the novel approach improves test accuracy and efficiency on several well-known symbolic regression problems.
Revised:  The experiments indicate that the novel approach improves training efficiency and reduces test errors on several well-known symbolic regression problems.
Edit intent: clarity
Original: There is an increasing number of works addressing the design challenge of fast, scalable solutions for the growing machine learning based application domain . Recently, most of the solutions aimed at improving processing element capabilities to speed up the execution of deep learning (DL) application .
Revised: There are increasing number of works addressing the design challenge of fast, scalable solutions for the growing machine learning based application domain . Recently, most of the solutions aimed at improving processing element capabilities to speed up the execution of deep learning (DL) application .
Edit intent: fluency
Original: There is an increasing number of works addressing the design challenge of fast, scalable solutions for the growing machine learning based application domain . Recently, most of the solutions aimed at improving processing element capabilities to speed up the execution of deep learning (DL) application .
Revised: There is an increasing number of works addressing the design challenges of fast, scalable solutions for the growing machine learning based application domain . Recently, most of the solutions aimed at improving processing element capabilities to speed up the execution of deep learning (DL) application .
Edit intent: fluency
Original: There is an increasing number of works addressing the design challenge of fast, scalable solutions for the growing machine learning based application domain . Recently, most of the solutions aimed at improving processing element capabilities to speed up the execution of deep learning (DL) application .
Revised: There is an increasing number of works addressing the design challenge of fast, scalable solutions for the growing machine learning based application domain . Recently, many of the solutions aimed at improving processing element capabilities to speed up the execution of deep learning (DL) application .
Edit intent: clarity
Original: There is an increasing number of works addressing the design challenge of fast, scalable solutions for the growing machine learning based application domain . Recently, most of the solutions aimed at improving processing element capabilities to speed up the execution of deep learning (DL) application .
Revised: There is an increasing number of works addressing the design challenge of fast, scalable solutions for the growing machine learning based application domain . Recently, most of the solutions aimed at improving processing element capabilities to speed up the execution of machine learning application domain .
Edit intent: clarity
Original:  Wrapping many cores together offer excellent parallelism, but it comes with multiple challenges (e.g., adequate interconnections).
Revised:  Wrapping many cores together offer excellent parallelism, but it brings other challenges (e.g., adequate interconnections).
Edit intent: clarity
Original:  In this paper, we propose a scalable and  efficient Network-on-Chip (NoC) architecture fusing the advantages of rings as well as the 2D-mesh without using any bridge router to provide high-performance.
Revised:  In this paper, we propose a scalable and efficient Network-on-Chip architecture fusing the advantages of rings as well as the 2D-mesh without using any bridge router to provide high-performance.
Edit intent: clarity
Original:  The running time of the exact decomposition algorithm is %DIFDELCMD < {\cal %%% O (|V|^2|E|) but is significantly faster in practice.
Revised:  The running time of the exact decomposition algorithm is %DIFDELCMD < {\cal %%% O (|V|^2|E|) but is significantly faster in practice.
Edit intent: fluency
Original: Backtracking line-search is an old yet powerful strategy for finding better step size to be used in proximal gradient algorithms.
Revised: Backtracking line-search is an old yet powerful strategy for finding a better step sizes to be used in proximal gradient algorithms.
Edit intent: fluency
Original:  This gives rise to a double convex-concave backtracking procedure which allows for an adaptive and optimal choice of both the step size and extrapolation parameters.
Revised:  This gives rise to a double convex-concave backtracking procedure which allows for an adaptive choice of both the step size and extrapolation parameters.
Edit intent: clarity
Original:  We apply this procedure to the class of inertial Bregman proximal gradient methods, and prove that any sequence generated  converges globally to critical points of the function at hand.
Revised:  We apply this procedure to the class of inertial Bregman proximal gradient methods, and prove that any sequence generated by these algorithms converges globally to critical points of the function at hand.
Edit intent: clarity
Original:  We apply this procedure to the class of inertial Bregman proximal gradient methods, and prove that any sequence generated  converges globally to critical points of the function at hand.
Revised:  We apply this procedure to the class of inertial Bregman proximal gradient methods, and prove that any sequence generated converges globally to a critical point of the function at hand.
Edit intent: fluency
Original:  While this category has a symmetric monoidal structure that describes doing processes in parallel, its fibers also have non-symmetric monoidal structures that describe doing one process and then another while reusing the catalysts.
Revised:  While this category has a symmetric monoidal structure that describes doing processes in parallel, its fibers also have premonoidal structures that describe doing one process and then another while reusing the catalysts.
Edit intent: clarity
Original:  Working with over 2.8M removed comments collected from 100 different communities on Reddit , we identify 8 macro norms (i.e., norms that are widely enforced on most parts of Reddit ) .
Revised:  Working with over 2.8M removed comments collected from 100 different communities on Reddit , we identify 8 macro norms---norms that are widely enforced on most parts of Reddit ) .
Edit intent: coherence
Original:  Working with over 2.8M removed comments collected from 100 different communities on Reddit , we identify 8 macro norms (i.e., norms that are widely enforced on most parts of Reddit ) .
Revised:  Working with over 2.8M removed comments collected from 100 different communities on Reddit , we identify 8 macro norms (i.e., norms that are widely enforced on most parts of Reddit .
Edit intent: fluency
Original:  We extract these macro norms by employing a hybrid approach (classification , topic modeling, and open-coding), on comments identified to be norm violations within at least 85 out of the 100 study subreddits.
Revised:  We extract these macro norms by employing a hybrid approach---classification , topic modeling, and open-coding), on comments identified to be norm violations within at least 85 out of the 100 study subreddits.
Edit intent: fluency
Original:  We extract these macro norms by employing a hybrid approach (classification , topic modeling, and open-coding), on comments identified to be norm violations within at least 85 out of the 100 study subreddits.
Revised:  We extract these macro norms by employing a hybrid approach (classification , topic modeling, and open-coding---on comments identified to be norm violations within at least 85 out of the 100 study subreddits.
Edit intent: fluency
Original: Morphogenesis in whole-body regeneration requires the dynamic interplay of three types of processes: biochemical, mechanical and electrical , which span all scales from the molecular to the entire organism.
Revised: Morphogenesis involves the dynamic integration of biochemical, mechanical and electrical , which span all scales from the molecular to the entire organism.
Edit intent: clarity
Original:  Remarkably, above this critical field morphogenesis exhibits reversal dynamics ;
Revised:  Remarkably, above this critical field morphogenesis exhibits reversal dynamics :
Edit intent: fluency
Original:  a fully developed animal flows back into its incipient spheroid morphology , which nevertheless can regenerate again when the amplitude of the external electric field is reduced  below criticality.
Revised:  a fully developed animal folds back into its incipient spheroid morphology , which nevertheless can regenerate again when the amplitude of the external electric field is reduced below criticality.
Edit intent: clarity
Original:  a fully developed animal flows back into its incipient spheroid morphology , which nevertheless can regenerate again when the amplitude of the external electric field is reduced  below criticality.
Revised:  a fully developed animal flows back into its incipient spheroid morphology . The potential to renew morphogenesis is re-exposed when the field is reduced below criticality.
Edit intent: clarity
Original:  a fully developed animal flows back into its incipient spheroid morphology , which nevertheless can regenerate again when the amplitude of the external electric field is reduced  below criticality.
Revised:  a fully developed animal flows back into its incipient spheroid morphology , which nevertheless can regenerate again when the amplitude of the external electric field is reduced back to amplitudes below criticality.
Edit intent: clarity
Original:  We further show that electric-induced reversal of morphogenesis is  triggered by enhanced electrical activity of the Hydra tissue .
Revised:  We further show that electric-induced reversal of morphogenesis is shown to be triggered by enhanced electrical activity of the Hydra tissue .
Edit intent: clarity
Original:  We further show that electric-induced reversal of morphogenesis is  triggered by enhanced electrical activity of the Hydra tissue .
Revised:  We further show that electric-induced reversal of morphogenesis is triggered by enhanced electrical excitations in the Hydra tissue .
Edit intent: clarity
Original: Morphogenesis involves the dynamic integration of biochemical, mechanical and electrical processes .
Revised: Morphogenesis involves the dynamic integration of different processes leading to the emergence of a viable animal .
Edit intent: clarity
Original: Morphogenesis involves the dynamic integration of different processesleading to the emergence of a viable animal.
Revised: Morphogenesis involves the dynamic interplay of biochemical, mechanical and electrical processes. Here we ask: to what extent can the course of morphogenesis be modulated and controlled by an external electric field?
Edit intent: clarity
Original:  Moreover, above a critical field amplitudemorphogenesis exhibits reversal dynamics: a fully developed animal folds back into its incipient spheroid morphology.
Revised:  Moreover, above this critical amplitude, the electric field can even lead to reversal dynamics: a fully developed animal folds back into its incipient spheroid morphology.
Edit intent: clarity