wanyu/IteraTeR_v2 huggingface dataset:
Original: In this article, we present a probabilistic algorithm to compute the product of two univariate sparse polynomials over a field with a number of bit operations that is quasi-linear in the size of the input and the output.
Revised: We present a probabilistic algorithm to compute the product of two univariate sparse polynomials over a field with a number of bit operations that is quasi-linear in the size of the input and the output.
Edit intent: clarity
Original:  Using Kronecker substitution techniques we are able to extend our result to the multivariate case.
Revised:  Using Kronecker substitution techniques we extend our result to the multivariate case.
Edit intent: clarity
Original: A set S \subseteq V is a dominating set in G if for every u \in V \setminus S, there exists v \in S such that (u,v) \in E, i.e., N[S] = V. A dominating set S is an Isolate Dominating Set (IDS  ) if the induced subgraph G[S] has at least one isolated vertex.
Revised: A set S \subseteq V is a dominating set in G if for every u \in V \setminus S, there exists v \in S such that (u,v) \in E, i.e., N[S] = V. A dominating set S is an Isolate Dominating Set (IDS ) if the induced subgraph G[S] has at least one isolated vertex.
Edit intent: fluency
Original: A set S \subseteq V is a dominating set in G if for every u \in V \setminus S, there exists v \in S such that (u,v) \in E, i.e., N[S] = V. A dominating set S is an Isolate Dominating Set (IDS  ) if the induced subgraph G[S] has at least one isolated vertex.
Revised: A set S \subseteq V is a dominating set in G if for every u \in V \ S, there exists v \in S such that (u,v) \in E, i.e., N[S] = V. A dominating set S is an Isolate Dominating Set (IDS ) if the induced subgraph G[S] has at least one isolated vertex.
Edit intent: clarity
Original: A set S \subseteq V is a dominating set in G if for every u \in V \setminus S, there exists v \in S such that (u,v) \in E, i.e., N[S] = V. A dominating set S is an Isolate Dominating Set (IDS  ) if the induced subgraph G[S] has at least one isolated vertex.
Revised: A set S \subseteq V is a dominating set in G if for every u \in V \setminus S, there exists v \in S such that (u,v) \in E, i.e., N[S] = V. A dominating set S is an Isolate Dominating Set IDS ) if the induced subgraph G[S] has at least one isolated vertex.
Edit intent: clarity
Original:  A set S \subseteq V is an independent set if G[S] has no edge.
Revised:  A set S \subseteq V is an independent set if G[S] has no edge.
Edit intent: fluency
Original:  A set S \subseteq V is a secure dominating set of G if, for each vertex u \in V \setminus S, there exists a vertex v \in S such that (u,v) \in E and (S \setminus \{v\}) \cup \{u\} is a dominating set of G. In addition, we initiate the study of a new domination parameter called, independent secure domination .
Revised:  A set S \subseteq V is a secure dominating set of G if, for each vertex u \in V \setminus S, there exists a vertex v \in S such that (u,v) \in E and (S \setminus \{v\}) \cup \{u\} is a dominating set of G. In addition, we initiate the study of a new domination parameter called, independent secure domination .
Edit intent: fluency
Original:  A set S \subseteq V is a secure dominating set of G if, for each vertex u \in V \setminus S, there exists a vertex v \in S such that (u,v) \in E and (S \setminus \{v\}) \cup \{u\} is a dominating set of G. In addition, we initiate the study of a new domination parameter called, independent secure domination .
Revised:  A set S \subseteq V is a secure dominating set of G if, for each vertex u \in V \setminus S, there exists a vertex v \in S such that (u,v) \in E and (S \ \{v\}) \cup \{u\} is a dominating set of G. In addition, we initiate the study of a new domination parameter called, independent secure domination .
Edit intent: clarity
Original:  A set S\subseteq V is an \textit{Independent Secure Dominating Set (\textit{InSDS ) if S is an independent set and a secure dominating set of G. The minimum size of an InSDS in G is called the \textit{independent secure domination number of G and is denoted by \gamma_{is}(G).
Revised:  A set S\subseteq V is an \textit{ (\textit{InSDS ) if S is an independent set and a secure dominating set of G. The minimum size of an InSDS in G is called the \textit{independent secure domination number of G and is denoted by \gamma_{is}(G).
Edit intent: clarity
Original:  A set S\subseteq V is an \textit{Independent Secure Dominating Set (\textit{InSDS ) if S is an independent set and a secure dominating set of G. The minimum size of an InSDS in G is called the \textit{independent secure domination number of G and is denoted by \gamma_{is}(G).
Revised:  A set S\subseteq V is an \textit{Independent Secure Dominating Set \textit{InSDS ) if S is an independent set and a secure dominating set of G. The minimum size of an InSDS in G is called the \textit{independent secure domination number of G and is denoted by \gamma_{is}(G).
Edit intent: clarity
Original:  A set S\subseteq V is an \textit{Independent Secure Dominating Set (\textit{InSDS ) if S is an independent set and a secure dominating set of G. The minimum size of an InSDS in G is called the \textit{independent secure domination number of G and is denoted by \gamma_{is}(G).
Revised:  A set S\subseteq V is an \textit{Independent Secure Dominating Set (\textit{Independent Secure Dominating Set (InSDS ) if S is an independent set and a secure dominating set of G. The minimum size of an InSDS in G is called the \textit{independent secure domination number of G and is denoted by \gamma_{is}(G).
Edit intent: fluency
Original:  A set S\subseteq V is an \textit{Independent Secure Dominating Set (\textit{InSDS ) if S is an independent set and a secure dominating set of G. The minimum size of an InSDS in G is called the \textit{independent secure domination number of G and is denoted by \gamma_{is}(G).
Revised:  A set S\subseteq V is an \textit{Independent Secure Dominating Set (\textit{InSDS ) if S is an independent set and a secure dominating set of G. The minimum size of an InSDS in G is called the \textit{independent secure domination number of G and is denoted by \gamma_{is}(G).
Edit intent: fluency
Original: Full waveform inversion (FWI) is today a standard process for the inverse problem of seismic imaging.
Revised: Full-waveform inversion (FWI) is today a standard process for the inverse problem of seismic imaging.
Edit intent: fluency
Original:  We then focus on two new issues beyond cycle skipping .
Revised:  We then focus on two new issues .
Edit intent: clarity
Original: The current two main methods for computing the numerical  are the level-set approach of Mengi and Overton and the cutting-plane method of Uhlig , but until now, no formal convergence rate results have been established for either.
Revised: The main two algorithms for computing the numerical are the level-set approach of Mengi and Overton and the cutting-plane method of Uhlig , but until now, no formal convergence rate results have been established for either.
Edit intent: clarity
Original: The current two main methods for computing the numerical  are the level-set approach of Mengi and Overton and the cutting-plane method of Uhlig , but until now, no formal convergence rate results have been established for either.
Revised: The current two main methods for computing the numerical are the level-set method of Mengi and Overton and the cutting-plane method of Uhlig , but until now, no formal convergence rate results have been established for either.
Edit intent: clarity
Original: We investigated the possibility to measure DNA supercoiling density (\sigma) along chromosomes using interaction frequencies between DNA and DNA-anchored clusters of proteins.
Revised: We investigate the measurement of DNA supercoiling density (\sigma) along chromosomes using interaction frequencies between DNA and DNA-anchored clusters of proteins.
Edit intent: clarity
Original:  Such a decomposition is essential in the q-analogous world of symbolic summation, for example, describing the q-counterpart of Ore-Sato theory or determining the applicability of the q-analogue of Zeilberger's algorithm to a q-hypergeometric term .
Revised:  Such a decomposition is essential in the q-analogous world of symbolic summation, for example, describing the q-counterpart of Ore-Sato theory .
Edit intent: clarity
Original: Recent developments in blockchain technology have inspired innovative new designs in distributed resilient database systems.
Revised: Recent developments in blockchain technology have inspired innovative new designs in resilient distributed and database systems.
Edit intent: clarity
Original:  At their core, these database systems typically use Byzantine fault-tolerant consensus protocols to maintain a common state across all replicas, even if some replicas are faulty or malicious.
Revised:  At their core, these blockchain applications typically use Byzantine fault-tolerant consensus protocols to maintain a common state across all replicas, even if some replicas are faulty or malicious.
Edit intent: clarity
Original:  To address this, we present the Geo-Scale Byzantine Fault-Tolerant consensus protocol (GeoBFT).
Revised:  To address this, we present the Geo-Scale Byzantine FaultTolerant consensus protocol (GeoBFT).
Edit intent: fluency
Original:  To validate our vision of high-performance geo-scale resilient database systemsusing GeoBFT , we implement GeoBFT in our efficient ResilientDB blockchain and database fabric.
Revised:  To validate our vision of high-performance geo-scale resilient distributed systems , we implement GeoBFT in our efficient ResilientDB blockchain and database fabric.
Edit intent: clarity
Original: Emotional voice conversion is to convert the spectrum and prosody to change the emotional patterns of speech, while preserving the speaker identity and linguistic content.
Revised: Emotional voice conversion aims to convert the spectrum and prosody to change the emotional patterns of speech, while preserving the speaker identity and linguistic content.
Edit intent: clarity
Original:  In this paper, we show that sequence models can do even better  when we improve the way a musical score is converted into events.
Revised:  In this paper, we show that sequence models can do even better for music modeling, when we improve the way a musical score is converted into events.
Edit intent: clarity
Original:  With this new approach, we build a Pop Music Transformer that composes Pop piano music with a more plausible rhythmic structure than prior arts do.
Revised:  With this approach, we build a Pop Music Transformer that composes Pop piano music with a more plausible rhythmic structure than prior arts do.
Edit intent: clarity
Original:  With this new approach, we build a Pop Music Transformer that composes Pop piano music with a more plausible rhythmic structure than prior arts do.
Revised:  With this new approach, we build a Pop Music Transformer that composes Pop piano music with better rhythmic structure than prior arts do.
Edit intent: clarity
Original: With the proliferation of ultra-high-speed mobile networks and internet-connected devices, along with the rise of artificial intelligence, the world is generating exponentially increasing amounts of data-data that needs to be processed in a fast, efficient and 'smart ' way.
Revised: With the proliferation of ultra-high-speed mobile networks and internet-connected devices, along with the rise of artificial intelligence, the world is generating exponentially increasing amounts of data - data that needs to be processed in a fast, efficient and 'smart ' way.
Edit intent: fluency
Original: With the proliferation of ultra-high-speed mobile networks and internet-connected devices, along with the rise of artificial intelligence, the world is generating exponentially increasing amounts of data-data that needs to be processed in a fast, efficient and 'smart ' way.
Revised: With the proliferation of ultra-high-speed mobile networks and internet-connected devices, along with the rise of artificial intelligence, the world is generating exponentially increasing amounts of data-data that needs to be processed in a fast, efficient and smart way.
Edit intent: fluency
Original:  Here, we demonstrate a computational specific integrated photonic tensor core-the optical analog of an ASIC-capable of operating at Tera-Multiply-Accumulate per second (TMAC/s) speeds.
Revised:  Here, we demonstrate a computational specific integrated photonic tensor core - the optical analog of an ASIC-capable of operating at Tera-Multiply-Accumulate per second (TMAC/s) speeds.
Edit intent: fluency
Original:  The computation is reduced to measuring the optical transmission of reconfigurable and non-resonant , i.e. broadband, passive components operating at a bandwidth exceeding 14 GHz, limited only by the speed of the modulators and photodetectors.
Revised:  The computation is reduced to measuring the optical transmission of reconfigurable and non-resonant passive components and can operate at a bandwidth exceeding 14 GHz, limited only by the speed of the modulators and photodetectors.
Edit intent: coherence
Original:  While we focus on convolution processing, more generally our results indicate the major potential of integrated photonics for parallel, fast, efficient and wafer-scale manufacturable computational hardware in demanding AI applications such as autonomous driving, live video processing, and next generation cloud computing services.
Revised:  While we focus on convolution processing, more generally our results indicate the major potential of integrated photonics for parallel, fast, and efficient computational hardware in demanding AI applications such as autonomous driving, live video processing, and next generation cloud computing services.
Edit intent: clarity
Original:  This work reviews with a critical and constructive attitude  our current knowledge of how genotypes map onto  phenotypes and organismal functions, and discusses theoretical and empirical avenues to broaden and improve this comprehension.
Revised:  This work delves into a critical and constructive attitude our current knowledge of how genotypes map onto phenotypes and organismal functions, and discusses theoretical and empirical avenues to broaden and improve this comprehension.
Edit intent: clarity
Original: This paper concerns the user scheduling problem in a multiuser multiple-input multi-output (MIMO) status update system, in which multiple single-antenna devices aim to send their latest statuses to a multiple-antenna information-fusion access point (AP) via a shared wireless channel.
Revised: This paper studies the user scheduling problem in a multiuser multiple-input multi-output (MIMO) status update system, in which multiple single-antenna devices aim to send their latest statuses to a multiple-antenna information-fusion access point (AP) via a shared wireless channel.
Edit intent: clarity
Original:  We aim to seek the optimal scheduling policy that can minimize the network-wide AoI by optimally deciding which device or group of devices to be scheduled for transmission in each slot given the instantaneous AoI values of all devices at the beginning of the said slot.
Revised:  We aim to seek the optimal scheduling policy that can minimize the network-wide AoI by optimally deciding which device or group of devices to be scheduled for transmission in each slot given the instantaneous AoI values of all devices at the beginning of the slot.
Edit intent: clarity
Original:  However , there is little work in understanding how directly changing the choice set can be used to influence a group's preferences or decisions .
Revised:  However , there is little work in understanding how directly changing the choice set can be used to influence the preferences of a collection of decision-makers .
Edit intent: clarity
Original:  Here, we use discrete choice modeling to develop an optimization framework of such interventions for several problems of group influence, including maximizing agreement or disagreement and promoting a particular choice.
Revised:  Here, we use discrete choice modeling to develop an optimization framework of such interventions for several problems of group influence, namely maximizing agreement or disagreement and promoting a particular choice.
Edit intent: clarity
Original:  We show that these problems are NP-hard in general  but imposing restrictions reveals a fundamental boundary: promoting an item is easier than maximizing agreement or disagreement.
Revised:  We show that these problems are NP-hard in general , but imposing restrictions reveals a fundamental boundary: promoting an item is easier than maximizing agreement or disagreement.
Edit intent: fluency
Original:  After, we design approximation algorithms for the hard problems and show that they work extremely well for real-world choice data.
Revised:  After, we design approximation algorithms for the hard problems and show that they work well on real-world choice data.
Edit intent: clarity
Original:  While there have been various proposals for encoding logical formulas into numerical vectors -- from simple strings to much more involved graph-based embeddings -- , little is known about how these different encodings compare.
Revised:  While there have been various proposals for encoding logical formulas into numerical vectors -- from simple strings to more involved graph-based embeddings -- , little is known about how these different encodings compare.
Edit intent: clarity
Original:  While there have been various proposals for encoding logical formulas into numerical vectors -- from simple strings to much more involved graph-based embeddings -- , little is known about how these different encodings compare.
Revised:  While there have been various proposals for encoding logical formulas into numerical vectors -- from simple strings to much more involved graph-based embeddings -- little is known about how these different encodings compare.
Edit intent: fluency
Original:  Our experiments show that some graph-based encodings help finding much shorter proofs and may yield better performance in terms of number of completed proofs.
Revised:  Our experiments show that the advantages of simpler encoding schemes in terms of number of completed proofs.
Edit intent: clarity
Original:  However, as expected, a detailed analysis shows the trade-offs in terms of runtime .
Revised:  However, as expected, a detailed analysis across several dimensions of theorem prover performance beyond just proof completion rate, thus providing empirical evidence to help guide future research on neural-guided theorem proving towards the most promising directions .
Edit intent: clarity
Original: We introduce a new multilevel ensemble Kalman filtering method (MLEnKF) which consists of a hierarchy of samples of the ensemble Kalman filter method (EnKF) using local-level Kalman gains .
Revised: We introduce a new multilevel ensemble Kalman filter method (MLEnKF) which consists of a hierarchy of samples of the ensemble Kalman filter method (EnKF) using local-level Kalman gains .
Edit intent: fluency
Original:  This new MLEnKF method is fundamentally different from the preexisting method introduced by Hoel, Law and Tempone in 2016, and it is also suitable for extensions towards multi-index Monte Carlo based filtering methods.
Revised:  This new MLEnKF method is fundamentally different from the preexisting method introduced by Hoel, Law and Tempone in 2016, and it is suitable for extensions towards multi-index Monte Carlo based filtering methods.
Edit intent: clarity
Original:  Robust theoretical analysis and supporting numerical examples show that under appropriate regularity assumptions, the MLEnKF method has better complexity asymptotically, in the large-ensemble and small-numerical-resolution limit , for weak approximations of quantities of interest than EnKF .
Revised:  Robust theoretical analysis and supporting numerical examples show that under appropriate regularity assumptions, the MLEnKF method has better complexity asymptotically, in the large-ensemble and fine-resolution limits , for weak approximations of quantities of interest than EnKF .
Edit intent: clarity
Original:  Robust theoretical analysis and supporting numerical examples show that under appropriate regularity assumptions, the MLEnKF method has better complexity asymptotically, in the large-ensemble and small-numerical-resolution limit , for weak approximations of quantities of interest than EnKF .
Revised:  Robust theoretical analysis and supporting numerical examples show that under appropriate regularity assumptions, the MLEnKF method has better complexity asymptotically, in the large-ensemble and small-numerical-resolution limit , for weak approximations of quantities of interest .
Edit intent: clarity
Original:  The method is developed for discrete-time filtering problems with a finite-dimensional state space and partial, linear observations polluted by additive Gaussian noise.
Revised:  The method is developed for discrete-time filtering problems with finite-dimensional state space and partial, linear observations polluted by additive Gaussian noise.
Edit intent: fluency
Original:  The method is developed for discrete-time filtering problems with a finite-dimensional state space and partial, linear observations polluted by additive Gaussian noise.
Revised:  The method is developed for discrete-time filtering problems with a finite-dimensional state space and linear observations polluted by additive Gaussian noise.
Edit intent: clarity
Original:  However, the fundamental assumptions underlying WMMA kinetics are usually violated in biomolecular contexts.
Edit intent: coherence
Original:  Which graph classes C exclude a fixed ladder as a minor?
Revised:  Which graph classes C exclude some ladder as a minor?
Edit intent: clarity
Original:  We show that every 3-connected graph with sufficiently many vertex-disjoint subgraphs containing a k ladder minor has a (k+1) -ladder minor.
Revised:  We show that every 3-connected graph with sufficiently many vertex-disjoint subgraphs each containing a \(k\)-ladder minor has a (k+1) -ladder minor.
Edit intent: clarity
Original:  We show that every 3-connected graph with sufficiently many vertex-disjoint subgraphs containing a k ladder minor has a (k+1) -ladder minor.
Revised:  We show that every 3-connected graph with sufficiently many vertex-disjoint subgraphs containing a k ladder minor has a \((k+1)\) -ladder minor.
Edit intent: coherence
Original: A k-ladder is a 2 \times k grid graph.
Revised: A ladder is a 2 \times k grid graph.
Edit intent: clarity
Original:  Which graph classes C exclude some ladder as a minor?
Revised:  When does a graph class C exclude some ladder as a minor?
Edit intent: clarity
Original:  there is a color that appears exactly once in H. If one were considering all connected subgraphs of G instead, then such a coloring is known as a centered coloring, and the minimum achievable number of colors  is the treedepth of G . Classes of graphs with bounded treedepth are exactly those that exclude a fixed path as a subgraph, or equivalently, as a minor.
Revised:  there is a color that appears exactly once in H. If one were considering all connected subgraphs of G instead, then such a coloring is known as a centered coloring, where for every connected subgraph H of G, there must be a color that appears exactly once in H. The minimum number of colors is the treedepth of G . Classes of graphs with bounded treedepth are exactly those that exclude a fixed path as a subgraph, or equivalently, as a minor.
Edit intent: clarity