wanyu/IteraTeR_v2 huggingface dataset:
Original: Real-time signal processing applications are increasingly focused on analyzing privacy-sensitive data obtained from individuals , and this data might need to be processed through model-based estimators to produce accurate statistics .
Revised: Real-time signal processing applications are increasingly focused on analyzing privacy-sensitive data obtained from individuals . To produce accurate statistics about the habits of a population of users of a system, this data might need to be processed through model-based estimators to produce accurate statistics .
Edit intent: clarity
Original: Real-time signal processing applications are increasingly focused on analyzing privacy-sensitive data obtained from individuals , and this data might need to be processed through model-based estimators to produce accurate statistics .
Revised: Real-time signal processing applications are increasingly focused on analyzing privacy-sensitive data obtained from individuals , and this data might need to be processed through model-based estimators .
Edit intent: clarity
Original:  Moreover, the models used in population dynamicsstudies, e.g., in epidemiology or sociology ,  are often necessarily nonlinear.
Revised:  Moreover, models of population dynamics , are often necessarily nonlinear.
Edit intent: clarity
Original: Aside from numerical algorithms and problem setup, large-scale physics simulations on distributed-memory supercomputersrequire more basic utilitarian functionality , such as physical units and constants;
Revised: Aside from numerical algorithms and problem setup, large-scale physics simulations on distributed memory supercomputers. This functionality includes physical units and constants;
Edit intent: clarity
Original: Cultural transmission of reproductive success states that successful men have more children and pass this greater fecundity to their offspring.
Revised: Cultural transmission of reproductive success states that successful men have more children and pass this raised fecundity to their offspring.
Edit intent: clarity
Original:  Hence, an explanation invoking cultural transmission of reproductive success is statistically unnecessary.
Revised:  Hence, explanations invoking cultural transmission of reproductive success is statistically unnecessary.
Edit intent: clarity
Original:  Hence, an explanation invoking cultural transmission of reproductive success is statistically unnecessary.
Revised:  Hence, an explanation invoking cultural transmission of reproductive success are statistically unnecessary.
Edit intent: fluency
Original:  Notably, this approach does not require specific constraints on the payoff function (e.g. convexity), and would appear to be generalisable to many related problems.
Revised:  Notably, this approach does not require specific constraints on the payoff function (e.g. convexity), and would appear to generalise to many related problems.
Edit intent: clarity
Original:  The proposed model is trained to simultaneously minimize the sum of supervised and unsupervised cost functions by backpropagation, avoiding the need for layer-wise pretraining .
Revised:  The proposed model is trained to simultaneously minimize the sum of supervised and unsupervised cost functions by backpropagation, avoiding the need for layer-wise pre-training .
Edit intent: fluency
Original:  Our work builds on top of the Ladder network proposed by Valpola (2015)  which we extend by combining the model with supervision.
Revised:  Our work builds on the Ladder network proposed by Valpola (2015) which we extend by combining the model with supervision.
Edit intent: fluency
Original:  Our work builds on top of the Ladder network proposed by Valpola (2015)  which we extend by combining the model with supervision.
Revised:  Our work builds on top of the Ladder network proposed by Valpola (2015) , which we extend by combining the model with supervision.
Edit intent: fluency
Original:  We show that the resulting model reaches state-of-the-art performance in various tasks: MNIST and CIFAR-10 classification in a semi-supervised setting and permutation invariant MNIST in both semi-supervised and full-labels setting .
Revised:  We show that the resulting model reaches state-of-the-art performance in semi-supervised MNIST and CIFAR-10 classification in a semi-supervised setting and permutation invariant MNIST in both semi-supervised and full-labels setting .
Edit intent: clarity
Original:  We show that the resulting model reaches state-of-the-art performance in various tasks: MNIST and CIFAR-10 classification in a semi-supervised setting and permutation invariant MNIST in both semi-supervised and full-labels setting .
Revised:  We show that the resulting model reaches state-of-the-art performance in various tasks: MNIST and CIFAR-10 classification , in addition to permutation-invariant MNIST classification with all labels .
Edit intent: clarity
Original: A plane tiling consisting of congruent copies of a shape is isohedral provided that for any pair of copies, there exists a symmetry of the tiling mapping one copy to the other.
Revised: A plane tiling consisting of congruent copies of a shape is isohedral provided that for any pair of copies, there exists a symmetry of the tiling mapping one copy to the other.
Edit intent: fluency
Original: It is shown that : (1) The problem of deciding positivity of Kronecker coefficients is NP-hard.
Revised: We show that the problem of deciding positivity of Kronecker coefficients is NP-hard.
Edit intent: coherence
Original:  Specifically, we show that, for } any 0<\epsilon %DIFDELCMD < \le %%% 1 \leq1 , there exists 0<a<1 such that, for all m, there exist \Omega(2^{m^a}) partition triples (\lambda,\mu,\mu) in the Kronecker cone such that: (a) the Kronecker coefficient k^\mu,\mu is zero, (b) the height of \mu is m, (c) the height of \lambda is \le m^\epsilon, and (d) |\lambda|=|\mu| \le m^3.
Revised:  Specifically, we show that, for } any 0<\epsilon %DIFDELCMD < \le %%% \leq1 , there exists 0<a<1 such that, for all m, there exist \Omega(2^{m^a}) partition triples (\lambda,\mu,\mu) in the Kronecker cone such that: (a) the Kronecker coefficient k^\mu,\mu is zero, (b) the height of \mu is m, (c) the height of \lambda is \le m^\epsilon, and (d) |\lambda|=|\mu| \le m^3.
Edit intent: clarity
Original:  Through a suitable Lyapunov functional we show that , for the linearized version of our system, for t\rightarrow +\infty, the migrating aggregate exponentially converge to a state in which all the particles have a same position with zero velocity.
Revised:  Through a suitable Lyapunov functional we show that for t\rightarrow +\infty, the migrating aggregate exponentially converge to a state in which all the particles have a same position with zero velocity.
Edit intent: clarity
Original:  Through a suitable Lyapunov functional we show that , for the linearized version of our system, for t\rightarrow +\infty, the migrating aggregate exponentially converge to a state in which all the particles have a same position with zero velocity.
Revised:  Through a suitable Lyapunov functional we show that , for the linearized version of our system, for t\rightarrow +\infty, the migrating aggregate exponentially converges to a state in which all the particles have a same position with zero velocity.
Edit intent: fluency
Original:  Finally, from the numerical point of view, some meaningful dynamical tests are proposed to simulate the behaviour of the system, also in comparison with the analytical findings .
Revised:  Finally, we present a comparison between the analytical findings and some numerical results, concerning the behaviour of the system, also in comparison with the analytical findings .
Edit intent: clarity
Original:  In Sketch-N-Sketch , the user first defines a program in a small functional language that generates an output SVG canvas , and may then may directly manipulate the canvas in two modes: live mode, which always keeps the program and canvas synchronized, or ad hoc mode, which temporarily allows larger, structural changes to the canvas before reconciling the changes with the program .
Revised:  In Sketch-N-Sketch , the user writes a program to generate an output SVG canvas , and may then may directly manipulate the canvas in two modes: live mode, which always keeps the program and canvas synchronized, or ad hoc mode, which temporarily allows larger, structural changes to the canvas before reconciling the changes with the program .
Edit intent: clarity
Original:  In Sketch-N-Sketch , the user first defines a program in a small functional language that generates an output SVG canvas , and may then may directly manipulate the canvas in two modes: live mode, which always keeps the program and canvas synchronized, or ad hoc mode, which temporarily allows larger, structural changes to the canvas before reconciling the changes with the program .
Revised:  In Sketch-N-Sketch , the user first defines a program in a small functional language that generates an output SVG canvas . Then the user may directly manipulate the canvas in two modes: live mode, which always keeps the program and canvas synchronized, or ad hoc mode, which temporarily allows larger, structural changes to the canvas before reconciling the changes with the program .
Edit intent: coherence
Original:  Our design for mitigating ambiguity allows us to implement a variety of examples using a novel and effective combination of programming and direct manipulation .
Revised:  Our design for mitigating ambiguity allows us to implement a variety of examples using a novel and effective workflow between the boundaries of existing programmatic and direct manipulation .
Edit intent: clarity
Original: We present the Sketch-n-Sketch editor for Scalable Vector Graphics (SVG) that integrates programmatic and direct manipulation , two modes of interaction with complementary strengths .
Revised: We present the Sketch-n-Sketch that integrates programmatic and direct manipulation , two modes of interaction with complementary strengths .
Edit intent: clarity
Original:  Then the user may directly manipulate the canvas while the system infers real-time updates to the program in order to match the changes to the output  .
Revised:  Then the user may directly manipulate the canvas while the system immediately infers a program update in order to match the changes to the output .
Edit intent: clarity
Original:  Based on our experience writing more than 40 examples and from the results of a study with 25 participants, we conclude that Sketch-n-Sketch provides a novel and effective workflow between the boundaries of existing programmatic and direct manipulation systems .
Revised:  Based on our experience writing more than 40 examples and from the results of a preliminary user study, we believe that Sketch-n-Sketch provides a novel and effective workflow between the boundaries of existing programmatic and direct manipulation systems .
Edit intent: clarity
Original:  Based on our experience writing more than 40 examples and from the results of a study with 25 participants, we conclude that Sketch-n-Sketch provides a novel and effective workflow between the boundaries of existing programmatic and direct manipulation systems .
Revised:  Based on our experience writing more than 40 examples and from the results of a study with 25 participants, we conclude that Sketch-n-Sketch provides a novel and effective workflow between the boundaries of existing programmatic and direct manipulation .
Edit intent: clarity
Original:  Numerical experiments showed that the proposed methods produced reasonable estimation with percentage errors mostly confined within a +/-10\% range for each eigenvalue .
Revised:  Numerical experiments showed that the proposed methods produced reasonable estimation with percentage errors confined within a +/-10\% range for each eigenvalue .
Edit intent: clarity
Original:  Numerical experiments showed that the proposed methods produced reasonable estimation with percentage errors mostly confined within a +/-10\% range for each eigenvalue .
Revised:  Numerical experiments showed that the proposed methods produced reasonable estimation with percentage errors mostly confined within a +/-10\% range for most eigenvalues .
Edit intent: clarity
Original: This paper presents methods to compare high order networks using persistent homology.
Edit intent: coherence
Original:  They can be considered as generalizations of conventional networks where only relationship functions between pairsare defined . Valid metric distances between high order networks have been defined but they are inherently difficult to compute when the number of nodes is large.
Revised:  They can be considered as generalizations of conventional networks where only relationship functions between pairsare defined . Valid metric distances between high order networks have been defined but they are difficult to compute when the number of nodes is large.
Edit intent: clarity
Original:  We relate high order networks to the filtrations of simplicial complexes and show that the difference between networks can be lower bounded by the difference between the homological features of their respective filtrations.
Revised:  We relate high order networks to filtrations of simplicial complexes and show that the difference between networks can be lower bounded by the difference between the homological features of their respective filtrations.
Edit intent: fluency
Original:  We relate high order networks to the filtrations of simplicial complexes and show that the difference between networks can be lower bounded by the difference between the homological features of their respective filtrations.
Revised:  We relate high order networks to the filtrations of simplicial complexes and showing that the distance between networks can be lower bounded by the difference between the homological features of their respective filtrations.
Edit intent: clarity
Original: Tur\'an problems in extremal combinatorics concern asymptotic bounds on the edge densities of graphs and hypergraphs that avoid specified subgraphs.
Revised: Tur\'an problems in extremal combinatorics ask to find asymptotic bounds on the edge densities of graphs and hypergraphs that avoid specified subgraphs.
Edit intent: clarity
Original:  The theory of flag algebras proposed by Razborov provides powerful semidefinite programming based methods to find sums of squares that establish edge density inequalities in Tur\'an problems.
Revised:  The theory of flag algebras proposed by Razborov provides powerful methods based on semidefinite programming to find sums of squares that establish edge density inequalities in Tur\'an problems.
Edit intent: clarity
Original:  Working with polynomial analogs of the flag algebra entities, we prove that the sums of squares created by flag algebras for Tur\'an problems can be retrieved from a restricted version of the symmetry-adapted semidefinite program proposed by Gatermann and Parrilo.
Revised:  Working with polynomial analogs of the flag algebra entities, we prove that such sums of squares created by flag algebras for Tur\'an problems can be retrieved from a restricted version of the symmetry-adapted semidefinite program proposed by Gatermann and Parrilo.
Edit intent: clarity
Original:  Working with polynomial analogs of the flag algebra entities, we prove that the sums of squares created by flag algebras for Tur\'an problems can be retrieved from a restricted version of the symmetry-adapted semidefinite program proposed by Gatermann and Parrilo.
Revised:  Working with polynomial analogs of the flag algebra entities, we prove that the sums of squares created by flag algebras can be retrieved from a restricted version of the symmetry-adapted semidefinite program proposed by Gatermann and Parrilo.
Edit intent: clarity
Original:  This connection reveals several combinatorial  properties of flag algebra sums of squares  and offers new tools for Tur\'an  problems.
Revised:  The connection reveals several combinatorial properties of flag algebra sums of squares and offers new tools for Tur\'an problems.
Edit intent: fluency
Original:  This connection reveals several combinatorial  properties of flag algebra sums of squares  and offers new tools for Tur\'an  problems.
Revised:  This connection reveals several combinatorial properties of flag algebra sums of squares , and offers new tools for Tur\'an problems.
Edit intent: fluency
Original:  These analogies are shown to derive from the fact that global variables undergo  stochastic bifurcation from the stochastically stable fixed point to continuous oscillations.
Revised:  These analogies are shown to derive from the fact that global variables undergo a stochastic bifurcation from the stochastically stable fixed point to continuous oscillations.
Edit intent: fluency
Original:  Local activation processes are analyzed in light of competition between the noise-led and the relaxation-driven dynamics.
Revised:  Local activation processes are analyzed in the light of the competition between the noise-led and the relaxation-driven dynamics.
Edit intent: fluency
Original: We consider the coaction of two distinct noise sources on the activation process of a single or two interacting excitable units represented by the Fitzhugh-Nagumo model.
Revised: We consider the coaction of two distinct noise sources on the activation process of a single and two interacting excitable units represented by the Fitzhugh-Nagumo model.
Edit intent: fluency
Original:  The key point lies in introducing the boundary conditions relevant for a class II excitable unit, which further allow an immediate generalization to scenarios involving a couple of units.
Revised:  The key point lies in introducing appropriate boundary conditions that are relevant for a class II excitable unit, which further allow an immediate generalization to scenarios involving a couple of units.
Edit intent: clarity
Original:  The key point lies in introducing the boundary conditions relevant for a class II excitable unit, which further allow an immediate generalization to scenarios involving a couple of units.
Revised:  The key point lies in introducing the boundary conditions relevant for a class II excitable unit, which can be immediately generalized also to scenarios involving a couple of units.
Edit intent: clarity
Original:  The key point lies in introducing the boundary conditions relevant for a class II excitable unit, which further allow an immediate generalization to scenarios involving a couple of units.
Revised:  The key point lies in introducing the boundary conditions relevant for a class II excitable unit, which further allow an immediate generalization to scenarios involving two coupled units.
Edit intent: clarity
Original:  We also analyze the effects of  two noise sources on the statistical features of the activation process,  demonstrating how these are modified due to the linear/nonlinear form of interactions.
Revised:  We analyze the effects of two noise sources on the statistical features of the activation process, demonstrating how these are modified due to the linear/nonlinear form of interactions.
Edit intent: clarity
Original:  We also analyze the effects of  two noise sources on the statistical features of the activation process,  demonstrating how these are modified due to the linear/nonlinear form of interactions.
Revised:  We also analyze the effects of the two noise sources on the statistical features of the activation process, demonstrating how these are modified due to the linear/nonlinear form of interactions.
Edit intent: fluency
Original:  We also analyze the effects of  two noise sources on the statistical features of the activation process,  demonstrating how these are modified due to the linear/nonlinear form of interactions.
Revised:  We also analyze the effects of two noise sources on the statistical features of the activation process, in particular demonstrating how these are modified due to the linear/nonlinear form of interactions.
Edit intent: clarity
Original:  Universal properties of  activation process are qualitatively discussed in light of stochastic bifurcation, underlying transition from stochastically stable fixed point to continuous oscillations.
Revised:  Universal properties of the activation process are qualitatively discussed in light of stochastic bifurcation, underlying transition from stochastically stable fixed point to continuous oscillations.
Edit intent: fluency
Original:  Universal properties of  activation process are qualitatively discussed in light of stochastic bifurcation, underlying transition from stochastically stable fixed point to continuous oscillations.
Revised:  Universal properties of activation process are qualitatively discussed in the light of a stochastic bifurcation that underlies the transition from a stochastically stable fixed point to continuous oscillations.
Edit intent: clarity
Original:  From recent work by Zetzsche this means that we can construct the downwards closure of the set of words accepted by a given HOPDA.
Revised:  From recent work by Zetzsche this means that we can construct the downward closure of the set of words accepted by a given HOPDA.
Edit intent: fluency
Original:  This also means we can construct the downwards closure of the Parikh image of a HOPDA.
Revised:  This also means we can construct the downward closure of the Parikh image of a HOPDA.
Edit intent: fluency
Original:  The Voronoi diagram for S is the subdivision of the plane into cells such that each cell has the same nearest neighbors in S. Classically, both structures can be computed in O(n \log n) time and O(n) space.
Revised:  The Voronoi diagram for S is the subdivision of the plane into cells such that all points in a cell have the same nearest neighbors in S. Classically, both structures can be computed in O(n \log n) time and O(n) space.
Edit intent: clarity
Original:  The Voronoi diagram for S is the subdivision of the plane into cells such that each cell has the same nearest neighbors in S. Classically, both structures can be computed in O(n \log n) time and O(n) space.
Revised:  The Voronoi diagram for S is the subdivision of the plane into cells such that each cell has the same nearest neighbor in S. Classically, both structures can be computed in O(n \log n) time and O(n) space.
Edit intent: fluency
Original:  The final result, "Network Literacy: Essential Concepts and Core Ideas", is now available as a booklet in several different languages from URL 
Revised:  The final result, "Network Literacy: Essential Concepts and Core Ideas", is now available as a booklet in several different languages from URL .
Edit intent: fluency
Original: Networks have become increasingly relevant to everyday life as our society has become increasingly connected.
Revised: Networks have become increasingly relevant to everyday life as human society has become increasingly connected.
Edit intent: clarity
Original:  Attaining a basic understanding of networks has thus become a necessary form of literacy for all people living in today's society (and for youths in particular).
Revised:  Attaining a basic understanding of networks has thus become a necessary form of literacy for people (and for youths in particular).
Edit intent: clarity
Original:  At the NetSci 2014 conference, we initiated a year-long process to develop an educational resource that concisely summarizes essential concepts about networks that can be used by anyone of school age and older.
Revised:  At the NetSci 2014 conference, we initiated a year-long process to develop an educational resource that concisely summarizes essential concepts about networks that can be used by anyone of school age or older.
Edit intent: fluency
Original:  We examined community structure in the concept network to group ideas into a set of important concepts , which we refined further through extensive discussion into seven essential concepts.
Revised:  We examined community structure in the concept network to group ideas into a set of important themes , which we refined further through extensive discussion into seven essential concepts.
Edit intent: clarity