wanyu/IteraTeR_v2 huggingface dataset:
Original:  Here we consider the computational complexity of natural questions about TBNs , and develop a practical algorithm for verifying the correctness of constructions by translating the problem into propositional logic and solving the resulting formula.
Revised:  Here we prove the computational hardness of natural questions about TBNs , and develop a practical algorithm for verifying the correctness of constructions by translating the problem into propositional logic and solving the resulting formula.
Edit intent: clarity
Original:  Here we consider the computational complexity of natural questions about TBNs , and develop a practical algorithm for verifying the correctness of constructions by translating the problem into propositional logic and solving the resulting formula.
Revised:  Here we consider the computational complexity of natural questions about TBNs and develop a practical algorithm for verifying the correctness of constructions by translating the problem into propositional logic and solving the resulting formula.
Edit intent: fluency
Original:  In particular, for each sufficiently large ineteger k, we introduce a class {\bf \Phi}_k of CNFs of (primal graph) treewidth at most k such that for any \varphi \in {\bf \Phi}_k and any Boolean function F \subseteq \varphi and such that |\varphi|/|F| \leq 2^{n} (here the functions are regarded as sets of assignments on which they are true), a NROBP implementing F is of size n^{\Omega(k \log n )}.
Revised:  In particular, for each sufficiently large ineteger k, we introduce a class {\bf \Phi}_k of CNFs of (primal graph) treewidth at most k such that for any \varphi \in {\bf \Phi}_k and any Boolean function F \subseteq \varphi and such that |\varphi|/|F| \leq 2^{n} (here the functions are regarded as sets of assignments on which they are true), a NROBP implementing F is of size n^{\Omega(k )}.
Edit intent: clarity
Original: In this paper, we propose two new deterministic interpolation algorithms for straight-line program multivariate polynomials .
Revised: In this paper, we propose new deterministic interpolation algorithms for straight-line program multivariate polynomials .
Edit intent: clarity
Original:  The algorithms have better complexities than existing determinist interpolation algorithms and have similar complexities with existing probabilistic algorithms  .
Revised:  The algorithms have better complexities than existing deterministic interpolation algorithms and have similar complexities with existing probabilistic algorithms .
Edit intent: fluency
Original:  Our Monte Carlo interpolation algorithms have better complexities than existing interpolation algorithms and are asymptotically optimal in the sense that their bit complexities are linear in the number of variables and the number of terms of the polynomials to be interpolated , when the coefficients of the polynomials are form a finite field  .
Revised:  Our Monte Carlo interpolation algorithms are asymptotically optimal in the sense that their bit complexities are linear in the number of variables and the number of terms of the polynomials to be interpolated , when the coefficients of the polynomials are form a finite field .
Edit intent: clarity
Original:  Our Monte Carlo interpolation algorithms have better complexities than existing interpolation algorithms and are asymptotically optimal in the sense that their bit complexities are linear in the number of variables and the number of terms of the polynomials to be interpolated , when the coefficients of the polynomials are form a finite field  .
Revised:  Our Monte Carlo interpolation algorithms have better complexities than existing interpolation algorithms and are asymptotically optimal in the sense that their bit complexities are linear in the number of variables and the number of terms of the polynomials to be interpolated , when the coefficients of the polynomials are from a finite field .
Edit intent: fluency
Original: In this paper, we propose new deterministic interpolation algorithms and Monte Carlo interpolation algorithms for sparse multivariate polynomials represented by straight-line programs.
Revised: In this paper, we propose new deterministic and Monte Carlo interpolation algorithms for sparse multivariate polynomials represented by straight-line programs.
Edit intent: fluency
Original:  Let f be an n-variate polynomial with a degree bound D and and term bound T.
Revised:  Let f be an n-variate polynomial with a degree bound D and a term bound T.
Edit intent: fluency
Original:  Our Monte Carlo interpolation algorithms are asymptotically optimal in the sense that their bit complexities are linear in nT and cubic in log D, when the coefficients of the polynomials are from a finite field.
Revised:  Our Monte Carlo interpolation algorithms have better complexities than existing Monte Carlo interpolation algorithms and are the first algorithms whose complexities are linear in nT and cubic in log D, when the coefficients of the polynomials are from a finite field.
Edit intent: clarity
Original: Based on an approach with bounded virtual exosystems, the output synchronization of heterogeneous linear networks is addressed.
Revised: In this paper, we address the output synchronization of heterogeneous linear networks is addressed.
Edit intent: clarity
Original:  All these aspects are demonstrated by an illustrative simulation example for which a detailed analysis is provided .
Revised:  All these aspects are demonstrated by an illustrative simulation example with a detailed analysis is provided .
Edit intent: clarity
Original:  All these aspects are demonstrated by an illustrative simulation example for which a detailed analysis is provided .
Revised:  All these aspects are demonstrated by an illustrative simulation example for which a detailed analysis .
Edit intent: clarity
Original: We present the first survey of its kind on results at the intersection of topological graph theory and the game of Cops and Robbers, focusing on results, conjectures, and open problems for the cop number of a graph embedded on a surface.
Revised: We survey results at the intersection of topological graph theory and the game of Cops and Robbers, focusing on results, conjectures, and open problems for the cop number of a graph embedded on a surface.
Edit intent: clarity
Original:  A multi-layer graph consists of a set of simple graphs , called layers, that all have the same vertex set .
Revised:  A multi-layer graph consists of a set of graphs on the same vertex set .
Edit intent: clarity
Original:  More specifically, we allow to mark at most d vertices and to transform each layer of the multi-layer graph into a cluster graph with at most k edge modifications per layer such that, if we remove the marked vertices, we obtain the same cluster graph in all layers.
Revised:  More specifically, we want to mark at most d vertices and to transform each layer of the multi-layer graph into a cluster graph with at most k edge modifications per layer such that, if we remove the marked vertices, we obtain the same cluster graph in all layers.
Edit intent: coherence
Original:  More specifically, we allow to mark at most d vertices and to transform each layer of the multi-layer graph into a cluster graph with at most k edge modifications per layer such that, if we remove the marked vertices, we obtain the same cluster graph in all layers.
Revised:  More specifically, we allow to mark at most d vertices and to transform each layer into a cluster graph with at most k edge modifications per layer such that, if we remove the marked vertices, we obtain the same cluster graph in all layers.
Edit intent: clarity
Original:  More specifically, we allow to mark at most d vertices and to transform each layer of the multi-layer graph into a cluster graph with at most k edge modifications per layer such that, if we remove the marked vertices, we obtain the same cluster graph in all layers.
Revised:  More specifically, we allow to mark at most d vertices and to transform each layer of the multi-layer graph into a cluster graph using at most k edge modifications per layer such that, if we remove the marked vertices, we obtain the same cluster graph in all layers.
Edit intent: clarity
Original:  More specifically, we allow to mark at most d vertices and to transform each layer of the multi-layer graph into a cluster graph with at most k edge modifications per layer such that, if we remove the marked vertices, we obtain the same cluster graph in all layers.
Revised:  More specifically, we allow to mark at most d vertices and to transform each layer of the multi-layer graph into a cluster graph with at most k edge additions or deletions per layer so that, if we remove the marked vertices, we obtain the same cluster graph in all layers.
Edit intent: clarity
Original: Next-generation sequencing techniques such as RNA-Seq allow cataloging of functional characteristics of microbial community members as well as their taxonomic identity.
Revised: High-throughput sequencing techniques such as RNA-Seq allow cataloging of functional characteristics of microbial community members as well as their taxonomic identity.
Edit intent: clarity
Original:  Such studies have found that a community's functional composition can be conserved more strictly across multiple sources of variation than taxonomic composition is.
Revised:  Such studies have found that a community's functional composition can be conserved more strictly across varying settings than taxonomic composition is.
Edit intent: clarity
Original:  I use a standard ecological resource-consumer model to examine the dynamics of traits relevant to resource consumption, and compare the dynamics of functional composition to the dynamics of taxonomic composition .
Revised:  I use a standard ecological resource-consumer model to examine the dynamics of traits relevant to resource consumption, and compare the dynamics of functional composition .
Edit intent: clarity
Original:  This model demonstrates that interaction with essential resources can regulate the community-wide abundance of related traits, keeping them at consistent levels despite large changes in the abundances of the species housing those traits in response to changes in the environment .
Revised:  This model demonstrates that interaction with essential resources can regulate the community-wide abundance of ecologically relevant traits, keeping them at consistent levels despite large changes in the abundances of the species housing those traits in response to changes in the environment .
Edit intent: clarity
Original:  This pattern of regulation is then shown to be connected to the functional form of the consumer species' responses to resource availability, changes in which can blunt and even reverse the contrast between the dynamics of functional and taxonomic composition .
Revised:  This pattern of regulation is then shown to be able to track differences in environmental conditions faithfully across differences in community composition. Mathematical conditions on consumers' vital rates and functional responses sufficient to produce conservation of functional community structure across taxonomic differences are presented .
Edit intent: clarity
Original: Sharing of social media datasets  presents the caveat that they are not always completely replicable.
Revised: With social media datasets presents the caveat that they are not always completely replicable.
Edit intent: clarity
Original: Sharing of social media datasets  presents the caveat that they are not always completely replicable.
Revised: Sharing of social media datasets presents the caveat that those datasets are not always completely replicable.
Edit intent: clarity
Original:  To quantify the impact of content deletion in the validity of datasets in a long term, we perform a longitudinal analysis of the persistence of 30 Twitter datasets, which include over 147 million tweets.
Revised:  To quantify the impact of content deletion in the replicability of datasets in a long term, we perform a longitudinal analysis of the persistence of 30 Twitter datasets, which include over 147 million tweets.
Edit intent: clarity
Original:  A map \varphi:G\rightarrow M is a weak embedding \textbf{ if it can be perturbed into an embedding \psi_\varepsilon:G\rightarrow M with \|\varphi-\psi_\varepsilon\|<\varepsilon for every \varepsilon> 0. A polynomial-time algorithm for recognizing weak embeddings was recently found by Fulek and Kyncl , 2017 , which reduces to solving a system of linear equations over Z_2.
Revised:  A map \varphi:G\rightarrow M is a \textbf{ if it can be perturbed into an embedding \psi_\varepsilon:G\rightarrow M with \|\varphi-\psi_\varepsilon\|<\varepsilon for every \varepsilon> 0. A polynomial-time algorithm for recognizing weak embeddings was recently found by Fulek and Kyncl , 2017 , which reduces to solving a system of linear equations over Z_2.
Edit intent: fluency
Original:  A map \varphi:G\rightarrow M is a weak embedding \textbf{ if it can be perturbed into an embedding \psi_\varepsilon:G\rightarrow M with \|\varphi-\psi_\varepsilon\|<\varepsilon for every \varepsilon> 0. A polynomial-time algorithm for recognizing weak embeddings was recently found by Fulek and Kyncl , 2017 , which reduces to solving a system of linear equations over Z_2.
Revised:  A map \varphi:G\rightarrow M is a weak embedding \textbf{weak embedding if it can be perturbed into an embedding \psi_\varepsilon:G\rightarrow M with \|\varphi-\psi_\varepsilon\|<\varepsilon for every \varepsilon> 0. A polynomial-time algorithm for recognizing weak embeddings was recently found by Fulek and Kyncl , 2017 , which reduces to solving a system of linear equations over Z_2.
Edit intent: clarity
Original:  A map \varphi:G\rightarrow M is a weak embedding \textbf{ if it can be perturbed into an embedding \psi_\varepsilon:G\rightarrow M with \|\varphi-\psi_\varepsilon\|<\varepsilon for every \varepsilon> 0. A polynomial-time algorithm for recognizing weak embeddings was recently found by Fulek and Kyncl , 2017 , which reduces to solving a system of linear equations over Z_2.
Revised:  A map \varphi:G\rightarrow M is a weak embedding \textbf{ if it can be perturbed into an embedding \psi_\varepsilon:G\rightarrow M with \|\varphi-\psi_\varepsilon\|<\varepsilon for every \varepsilon> 0. A polynomial-time algorithm for recognizing weak embeddings has recently been found by Fulek and Kyncl , 2017 , which reduces to solving a system of linear equations over Z_2.
Edit intent: fluency
Original:  A map \varphi:G\rightarrow M is a weak embedding \textbf{ if it can be perturbed into an embedding \psi_\varepsilon:G\rightarrow M with \|\varphi-\psi_\varepsilon\|<\varepsilon for every \varepsilon> 0. A polynomial-time algorithm for recognizing weak embeddings was recently found by Fulek and Kyncl , 2017 , which reduces to solving a system of linear equations over Z_2.
Revised:  A map \varphi:G\rightarrow M is a weak embedding \textbf{ if it can be perturbed into an embedding \psi_\varepsilon:G\rightarrow M with \|\varphi-\psi_\varepsilon\|<\varepsilon for every \varepsilon> 0. A polynomial-time algorithm for recognizing weak embeddings was recently found by Fulek and Kyncl , which reduces to solving a system of linear equations over Z_2.
Edit intent: clarity
Original:  A map \varphi:G\rightarrow M is a weak embedding \textbf{ if it can be perturbed into an embedding \psi_\varepsilon:G\rightarrow M with \|\varphi-\psi_\varepsilon\|<\varepsilon for every \varepsilon> 0. A polynomial-time algorithm for recognizing weak embeddings was recently found by Fulek and Kyncl , 2017 , which reduces to solving a system of linear equations over Z_2.
Revised:  A map \varphi:G\rightarrow M is a weak embedding \textbf{ if it can be perturbed into an embedding \psi_\varepsilon:G\rightarrow M with \|\varphi-\psi_\varepsilon\|<\varepsilon for every \varepsilon> 0. A polynomial-time algorithm for recognizing weak embeddings was recently found by Fulek and Kyncl , 2017 . It reduces the problem to solving a system of linear equations over Z_2.
Edit intent: clarity
Original:  Our algorithm is also conceptually simpler than Fulek and Kyn\v{c : We perform a sequence of local operations that gradually "untangles" the image \varphi(G) into an embedding \psi(G), or reports that \varphi is not a weak embedding.
Revised:  Our algorithm is also conceptually simpler Fulek and Kyn\v{c : We perform a sequence of local operations that gradually "untangles" the image \varphi(G) into an embedding \psi(G), or reports that \varphi is not a weak embedding.
Edit intent: coherence
Original:  Our algorithm is also conceptually simpler than Fulek and Kyn\v{c : We perform a sequence of local operations that gradually "untangles" the image \varphi(G) into an embedding \psi(G), or reports that \varphi is not a weak embedding.
Revised:  Our algorithm is also conceptually simpler than : We perform a sequence of local operations that gradually "untangles" the image \varphi(G) into an embedding \psi(G), or reports that \varphi is not a weak embedding.
Edit intent: coherence
Original:  We suggest that the distance between the fingerprints be measured as a weighted L2 norm of their difference.
Revised:  We propose that the 'distance' between the fingerprints be measured as a weighted L2 norm of their difference.
Edit intent: style
Original:  We suggest that the distance between the fingerprints be measured as a weighted L2 norm of their difference.
Revised:  We suggest that the distance between the fingerprints be measured as a weighted L_2 norm of their difference.
Edit intent: clarity
Original: Molecular fingerprints, i.e. feature vectors describing atomistic neighborhood configurations, is an important abstraction and a key ingredient for data-driven modeling of molecular energy and interatomic force.
Revised: Molecular fingerprints, i.e. feature vectors describing atomistic neighborhood configurations, is an important abstraction and a key ingredient for data-driven modeling of potential energy surface and interatomic force.
Edit intent: clarity
Original:  We propose that the 'distance' between the fingerprints be measured as a weighted L_2 norm of their difference.
Edit intent: coherence
Original:  Rotational invariance of the fingerprint is achieved by aligning, for each fingerprint instance, the neighboring atoms onto a set of local canonical coordinate frame computed from a kernel minisum optimization procedure.
Revised:  Rotational invariance of the fingerprint is achieved by aligning, for each fingerprint instance, the neighboring atoms onto a local canonical coordinate frame computed from a kernel minisum optimization procedure.
Edit intent: clarity
Original:  The applicability of the fingerprint is demonstrated through a set of realistic benchmark problems.
Revised:  The applicability of the fingerprint is demonstrated through a set of benchmark problems.
Edit intent: clarity
Original: Stochastic Spiking Neural Networks based on nanoelectronic spin devices can be a possible pathway at achieving " brain-like " compact and energy-efficient cognitive intelligence.
Revised: Stochastic spiking neural networks based on nanoelectronic spin devices can be a possible pathway at achieving " brain-like " compact and energy-efficient cognitive intelligence.
Edit intent: fluency
Original: Stochastic Spiking Neural Networks based on nanoelectronic spin devices can be a possible pathway at achieving " brain-like " compact and energy-efficient cognitive intelligence.
Revised: Stochastic Spiking Neural Networks based on nanoelectronic spin devices can be a possible pathway to achieving " brain-like " compact and energy-efficient cognitive intelligence.
Edit intent: fluency
Original: Stochastic Spiking Neural Networks based on nanoelectronic spin devices can be a possible pathway at achieving " brain-like " compact and energy-efficient cognitive intelligence.
Revised: Stochastic Spiking Neural Networks based on nanoelectronic spin devices can be a possible pathway at achieving " brainlike " compact and energy-efficient cognitive intelligence.
Edit intent: fluency
Original: Stochastic Spiking Neural Networks based on nanoelectronic spin devices can be a possible pathway at achieving " brain-like " compact and energy-efficient cognitive intelligence.
Revised: Stochastic Spiking Neural Networks based on nanoelectronic spin devices can be a possible pathway at achieving " brain-like " compact and energy-effcient cognitive intelligence.
Edit intent: fluency
Original:  This work attempts to explore the design space and analyze the performance of nano-magnet based stochastic neuromorphic computing architectures for magnets with different barrier heights.
Revised:  This work attempts to explore the design space and analyze the performance of nanomagnet-based stochastic neuromorphic computing architectures for magnets with different barrier heights.
Edit intent: fluency
Original:  We perform a device to system level analysis on a deep neural network architecture for a digit recognition problem on the MNIST dataset .
Revised:  We perform a device-to-system-level analysis on a deep neural network architecture for a digit recognition problem on the MNIST dataset .
Edit intent: fluency
Original:  We perform a device to system level analysis on a deep neural network architecture for a digit recognition problem on the MNIST dataset .
Revised:  We perform a device to system level analysis on a deep neural-network architecture for a digit recognition problem on the MNIST dataset .
Edit intent: fluency
Original:  We perform a device to system level analysis on a deep neural network architecture for a digit recognition problem on the MNIST dataset .
Revised:  We perform a device to system level analysis on a deep neural network architecture for a digit-recognition problem on the MNIST dataset .
Edit intent: fluency
Original:  We perform a device to system level analysis on a deep neural network architecture for a digit recognition problem on the MNIST dataset .
Revised:  We perform a device to system level analysis on a deep neural network architecture for a digit recognition problem on the MNIST data set .
Edit intent: clarity
Original:  Analyses often reveal abundant discordances among phylo- genies of different parts of genomes, as well as incongruences between species trees obtained using different methods or data partitions.
Revised:  Analyses often reveal abundant discordances among phylogenies of different parts of genomes, as well as incongruences between species trees obtained using different methods or data partitions.
Edit intent: fluency
Original:  Interpretive ways of measur- ing and visualizing discordance are needed, both among alternative species trees and gene trees, especially for specific focal branches of a tree.
Revised:  Interpretive ways of measuring and visualizing discordance are needed, both among alternative species trees and gene trees, especially for specific focal branches of a tree.
Edit intent: fluency
Original: In recent years, techniques based on convex optimization and real algebra that produce converging hierarchies of lower bounds for polynomial optimization problems (POPs) have gained much popularity.
Revised: In recent years, techniques based on convex optimization and real algebra that produce converging hierarchies of lower bounds for polynomial minimization problems have gained much popularity.
Edit intent: clarity
Original:  More precisely, we show that any inner approximation to the cone of positive homogeneous polynomials that is arbitrarily tight can be turned into a converging hierarchy  for general polynomial optimization problems with compact feasible sets.
Revised:  More precisely, we show that any inner approximation to the cone of positive homogeneous polynomials that is arbitrarily tight can be turned into a converging hierarchy for general polynomial minimization problems with compact feasible sets.
Edit intent: clarity
Original: The large variation in seed mass among species inspired a vast array of theoretical and empirical research that attempt to explain this variation.
Revised: The large variation in seed mass among species inspired a vast array of theoretical and empirical research attempting to explain this variation.
Edit intent: coherence