wanyu/IteraTeR_v2 huggingface dataset:
Original:  In this paper we close the space-time tradeoff exhibited in \mbox{ mastrolilli2006hybrid by designing a new FPTAS with a running time of O(n)  + (z^{2\cdot \max\{K,\varepsilon} /\varepsilon} ^{ -2 } \} ), while simultaneously reaching the O(n+z^{2/\varepsilon) space complexity .
Revised:  In this paper we close the space-time tradeoff exhibited in \mbox{ mastrolilli2006hybrid by designing a new FPTAS with a running time of O(n) + (z^{2\cdot \max\{K,\varepsilon} /\varepsilon} ^{ -2 } \} ), while simultaneously reaching the O(n+z^{2/\varepsilon) space bound .
Edit intent: clarity
Original:  An salient feature of our algorithm is that it is the \emph{first FPTAS, which achieves better time and space complexity bounds than the very first standard FPTAS \emph{over all parameter regimes .
Revised:  An salient feature of our scheme is that it is the \emph{first FPTAS, which achieves better time and space complexity bounds than the very first standard FPTAS \emph{over all parameter regimes .
Edit intent: clarity
Original:  An salient feature of our algorithm is that it is the \emph{first FPTAS, which achieves better time and space complexity bounds than the very first standard FPTAS \emph{over all parameter regimes .
Revised:  An salient feature of our algorithm is that it is the \emph{first FPTAS, which achieves better time and space complexity bounds than the very first standard FPTAS \emph{over all parameter regimes .
Edit intent: fluency
Original:  This problem is of fundamental importance and is known to have a broad range of applications in various fields such as computer science and operation research .
Revised:  This problem is of fundamental importance and is known to have a broad range of applications in various fields .
Edit intent: clarity
Original:  In this paper we close the space-time tradeoff exhibited in \mbox{ mastrolilli2006hybrid by designing a new FPTAS with a run-time of O(n+z^{2}/\varepsilon^{2}), while simultaneously reaching the O(n+z^{2}/\varepsilon) space bound.
Revised:  In this paper we close the space-time tradeoff exhibited in the state-of-the-art by designing a new FPTAS with a run-time of O(n+z^{2}/\varepsilon^{2}), while simultaneously reaching the O(n+z^{2}/\varepsilon) space bound.
Edit intent: clarity
Original:  Our scheme provides O(K) and O(z) improvements on the long-established state-of-the-art algorithms in time and space complexity respectively, and is the first scheme that achieves a run-time that is asymptotically independent of cardinality bound K  under fixed \varepsilon.
Revised:  Our scheme provides O(K) and O(z) improvements on the state-of-the-art algorithms in time and space complexity respectively, and is the first scheme that achieves a run-time that is asymptotically independent of cardinality bound K under fixed \varepsilon.
Edit intent: clarity
Original:  Our scheme provides O(K) and O(z) improvements on the long-established state-of-the-art algorithms in time and space complexity respectively, and is the first scheme that achieves a run-time that is asymptotically independent of cardinality bound K  under fixed \varepsilon.
Revised:  Our scheme provides O(K) and O(z) improvements on the long-established state-of-the-art algorithms in time and space complexity respectively, and is the first scheme that achieves a run-time that is independent of cardinality bound K under fixed \varepsilon.
Edit intent: clarity
Original:  Another salient feature of our scheme is that it is the first FPTAS , which achieves better time and space complexity bounds than the very first standard FPTAS over all parameter regimes.
Revised:  Another salient feature of our scheme is that it is the first FPTAS that achieves better time and space complexity bounds than the very first standard FPTAS over all parameter regimes.
Edit intent: coherence
Original:  In the bistable region , noise can switch between rest and spiking, and thus increase the variability of the spike train compared to neurons with only one stable attractor.
Revised:  In the bistable region , noise can induce switches between the attractors, i.e., between rest and spiking, and thus increase the variability of the spike train compared to neurons with only one stable attractor.
Edit intent: clarity
Original:  Switching between rest and spiking is mainly determined along the downstroke of the action potential , a dynamical feature lacking in common neuron modelswith reset dynamics.
Revised:  Switching between rest and spiking is mainly determined along the downstroke of the action potential -- a dynamical feature lacking in common neuron modelswith reset dynamics.
Edit intent: fluency
Original: We formulate gradient-based Markov chain Monte Carlo (MCMC) sampling as optimization on the space of probability measures, with Kullback-Leibler (KL) divergence as the objective function .
Revised: We formulate gradient-based Markov chain Monte Carlo (MCMC) sampling as optimization on the space of probability measures, with Kullback-Leibler (KL) divergence as the objective functional .
Edit intent: fluency
Original:  We show that an underdamped form of the Langevin algorithm perform accelerated gradient descent in this metric.
Revised:  We show that an underdamped form of the Langevin algorithm performs accelerated gradient descent in this metric.
Edit intent: fluency
Original:  Epileptic seizure type not only impacts on the choice of drugs but also on the range of activities a patient can safely engage in.
Revised:  Epileptic seizure types not only impact the choice of drugs but also on the range of activities a patient can safely engage in.
Edit intent: fluency
Original:  Epileptic seizure type not only impacts on the choice of drugs but also on the range of activities a patient can safely engage in.
Revised:  Epileptic seizure type not only impacts on the choice of drugs but also the range of activities a patient can safely engage in.
Edit intent: fluency
Original:  On that note, in this paper, we undertake the first study to explore the application of machine learning algorithms for multi-class seizure type classification.
Revised:  On that note, in this paper, we explore the application of machine learning algorithms for multi-class seizure type classification.
Edit intent: clarity
Original:  In particular, existing generalization bounds for RNNs mostly scale exponentially with the length of the input sequence, which limited their practical implications.
Revised:  In particular, existing generalization bounds for RNN scale exponentially with the length of the input sequence, which limited their practical implications.
Edit intent: clarity
Original:  In particular, existing generalization bounds for RNNs mostly scale exponentially with the length of the input sequence, which limited their practical implications.
Revised:  In particular, existing generalization bounds for RNNs mostly scale exponentially with the input length, significantly limiting their practical implications.
Edit intent: clarity
Original:  In this paper, we show that if the input labels are (approximately) realizable by certain classes of (non-linear) functions of the input sequences, then using the vanilla stochastic gradient descent (SGD), RNNs can actually learn themefficiently , meaning that both the training time and sample complexity only scalepolynomially with the input length (or almost polynomially, depending on the classes of non-linearity) .
Revised:  In this paper, we show using the vanilla stochastic gradient descent (SGD), RNNs can actually learn themefficiently , meaning that both the training time and sample complexity only scalepolynomially with the input length (or almost polynomially, depending on the classes of non-linearity) .
Edit intent: clarity
Original:  In this paper, we show that if the input labels are (approximately) realizable by certain classes of (non-linear) functions of the input sequences, then using the vanilla stochastic gradient descent (SGD), RNNs can actually learn themefficiently , meaning that both the training time and sample complexity only scalepolynomially with the input length (or almost polynomially, depending on the classes of non-linearity) .
Revised:  In this paper, we show that if the input labels are (approximately) realizable by certain classes of (non-linear) functions of the input sequences, then using the vanilla stochastic gradient descent (SGD), RNN can actually learn themefficiently , meaning that both the training time and sample complexity only scalepolynomially with the input length (or almost polynomially, depending on the classes of non-linearity) .
Edit intent: clarity
Original:  In this paper, we show that if the input labels are (approximately) realizable by certain classes of (non-linear) functions of the input sequences, then using the vanilla stochastic gradient descent (SGD), RNNs can actually learn themefficiently , meaning that both the training time and sample complexity only scalepolynomially with the input length (or almost polynomially, depending on the classes of non-linearity) .
Revised:  In this paper, we show that if the input labels are (approximately) realizable by certain classes of (non-linear) functions of the input sequences, then using the vanilla stochastic gradient descent (SGD), RNNs can actually learn efficiently , meaning that both the training time and sample complexity only scalepolynomially with the input length (or almost polynomially, depending on the classes of non-linearity) .
Edit intent: fluency
Original:  In this paper, we show that if the input labels are (approximately) realizable by certain classes of (non-linear) functions of the input sequences, then using the vanilla stochastic gradient descent (SGD), RNNs can actually learn themefficiently , meaning that both the training time and sample complexity only scalepolynomially with the input length (or almost polynomially, depending on the classes of non-linearity) .
Revised:  In this paper, we show that if the input labels are (approximately) realizable by certain classes of (non-linear) functions of the input sequences, then using the vanilla stochastic gradient descent (SGD), RNNs can actually learn themefficiently , meaning that both time and sample complexity only scalepolynomially with the input length (or almost polynomially, depending on the classes of non-linearity) .
Edit intent: clarity
Original:  In this paper, we show that if the input labels are (approximately) realizable by certain classes of (non-linear) functions of the input sequences, then using the vanilla stochastic gradient descent (SGD), RNNs can actually learn themefficiently , meaning that both the training time and sample complexity only scalepolynomially with the input length (or almost polynomially, depending on the classes of non-linearity) .
Revised:  In this paper, we show that if the input labels are (approximately) realizable by certain classes of (non-linear) functions of the input sequences, then using the vanilla stochastic gradient descent (SGD), RNNs can actually learn themefficiently , meaning that both the training time and sample complexity polynomially with the input length (or almost polynomially, depending on the classes of non-linearity) .
Edit intent: clarity
Original:  In this paper, we show that if the input labels are (approximately) realizable by certain classes of (non-linear) functions of the input sequences, then using the vanilla stochastic gradient descent (SGD), RNNs can actually learn themefficiently , meaning that both the training time and sample complexity only scalepolynomially with the input length (or almost polynomially, depending on the classes of non-linearity) .
Revised:  In this paper, we show that if the input labels are (approximately) realizable by certain classes of (non-linear) functions of the input sequences, then using the vanilla stochastic gradient descent (SGD), RNNs can actually learn themefficiently , meaning that both the training time and sample complexity only scale with the input length (or almost polynomially, depending on the classes of non-linearity) .
Edit intent: fluency
Original:  In this paper, we show that if the input labels are (approximately) realizable by certain classes of (non-linear) functions of the input sequences, then using the vanilla stochastic gradient descent (SGD), RNNs can actually learn themefficiently , meaning that both the training time and sample complexity only scalepolynomially with the input length (or almost polynomially, depending on the classes of non-linearity) .
Revised:  In this paper, we show that if the input labels are (approximately) realizable by certain classes of (non-linear) functions of the input sequences, then using the vanilla stochastic gradient descent (SGD), RNNs can actually learn themefficiently , meaning that both the training time and sample complexity only scalepolynomially scale polynomially in the input length (or almost polynomially, depending on the classes of non-linearity) .
Edit intent: clarity
Original:  In this paper, we apply string-processing techniques (specifically, prefix-sorting ) to speed up solutions for this problem on languages described by particular finite automata.
Revised:  In this paper, we combine techniques from string processing (specifically, prefix-sorting ) to speed up solutions for this problem on languages described by particular finite automata.
Edit intent: clarity
Original:  In this paper, we apply string-processing techniques (specifically, prefix-sorting ) to speed up solutions for this problem on languages described by particular finite automata.
Revised:  In this paper, we apply string-processing techniques (specifically, ) to speed up solutions for this problem on languages described by particular finite automata.
Edit intent: coherence
Original:  In this paper, we apply string-processing techniques (specifically, prefix-sorting ) to speed up solutions for this problem on languages described by particular finite automata.
Revised:  In this paper, we apply string-processing techniques (specifically, prefix-sorting ) to speed up solutions for this problem on languages described by finite automata.
Edit intent: clarity
Original:  the recent notion of Wheeler graph extends this concept to labeled graphs (for example, finite-state automata ) . A Wheeler graph admits a co-lexicographic ordering of its nodes and opens up the possibility of building fast and small data structures supporting  path queries on the graph . However, while strings and trees can always be prefix-sorted in linear time, the situation on  graphs is more complicated:
Revised:  the recent notion of Wheeler graph extends this concept to labeled graphs (for example, finite-state automata ) . A Wheeler graph admits a co-lexicographic ordering of its nodes and opens up the possibility of building fast and small data structures supporting path queries on the graph . However, while strings and trees can always be prefix-sorted in linear time, the situation on graphs is more complicated:
Edit intent: fluency
Original:  the recent notion of Wheeler graph extends this concept to labeled graphs (for example, finite-state automata ) . A Wheeler graph admits a co-lexicographic ordering of its nodes and opens up the possibility of building fast and small data structures supporting  path queries on the graph . However, while strings and trees can always be prefix-sorted in linear time, the situation on  graphs is more complicated:
Revised:  the recent notion of Wheeler graph extends this concept to labeled graphs such as finite-state automata ) . A Wheeler graph admits a co-lexicographic ordering of its nodes and opens up the possibility of building fast and small data structures supporting path queries on the graph . However, while strings and trees can always be prefix-sorted in linear time, the situation on graphs is more complicated:
Edit intent: clarity
Original:  the recent notion of Wheeler graph extends this concept to labeled graphs (for example, finite-state automata ) . A Wheeler graph admits a co-lexicographic ordering of its nodes and opens up the possibility of building fast and small data structures supporting  path queries on the graph . However, while strings and trees can always be prefix-sorted in linear time, the situation on  graphs is more complicated:
Revised:  the recent notion of Wheeler graph extends this concept to labeled graphs (for example, finite-state automata . A Wheeler graph admits a co-lexicographic ordering of its nodes and opens up the possibility of building fast and small data structures supporting path queries on the graph . However, while strings and trees can always be prefix-sorted in linear time, the situation on graphs is more complicated:
Edit intent: fluency
Original:  the recent notion of Wheeler graph extends this concept to labeled graphs (for example, finite-state automata ) . A Wheeler graph admits a co-lexicographic ordering of its nodes and opens up the possibility of building fast and small data structures supporting  path queries on the graph . However, while strings and trees can always be prefix-sorted in linear time, the situation on  graphs is more complicated:
Revised:  the recent notion of Wheeler graph extends this concept to labeled graphs (for example, finite-state automata ) . A Wheeler graph admits a co-lexicographic ordering of its nodes and opens up the possibility of building fast and small data structures supporting powerful path queries on the graph . However, while strings and trees can always be prefix-sorted in linear time, the situation on graphs is more complicated:
Edit intent: clarity
Original:  the recent notion of Wheeler graph extends this concept to labeled graphs (for example, finite-state automata ) . A Wheeler graph admits a co-lexicographic ordering of its nodes and opens up the possibility of building fast and small data structures supporting  path queries on the graph . However, while strings and trees can always be prefix-sorted in linear time, the situation on  graphs is more complicated:
Revised:  the recent notion of Wheeler graph extends this concept to labeled graphs (for example, finite-state automata ) . A Wheeler graph admits a co-lexicographic ordering of its nodes and opens up the possibility of building fast and small data structures supporting path queries on the graph . However, while strings and trees can always be prefix-sorted in linear time, the situation on general graphs is more complicated:
Edit intent: clarity
Original:  not all graphs are Wheeler , and a recent result shows that the problem of identifying them is NP-complete even for acyclic NFAs.
Revised:  not all graphs admit such an ordering , and a recent result shows that the problem of identifying them is NP-complete even for acyclic NFAs.
Edit intent: clarity
Original:  (i) we show that the problem of recognizing and sorting Wheeler DFAs (even cyclic)can be solved offline in optimal linear time , (ii)
Revised:  (i) recognize and prefix-sort Wheeler finite automata (even admitting some limited amount of nondeterminism) , (ii)
Edit intent: clarity
Original:  when the DFA is acyclic, we give an online algorithm that, when fed with the DFA's states in any topological order, with logarithmic delay computes the co-lexicographic rank of a new incoming state or decides that such an ordering does not exist, and (iii) we show that also Wheeler 2-NFAs---i.e. those with at most two equally-labeled transitions leaving any state---admit a polynomial-time identification and prefix-sorting algorithm.
Revised:  minimize Wheeler DFAs, and (iii) we show that also Wheeler 2-NFAs---i.e. those with at most two equally-labeled transitions leaving any state---admit a polynomial-time identification and prefix-sorting algorithm.
Edit intent: clarity
Original: Being able to efficiently test the membership of a word in a formal language is, arguably, one of the most fundamental problemsin computer science.
Revised: Indexing strings via prefix (or suffix) sorting is, arguably, one of the most fundamental problemsin computer science.
Edit intent: clarity
Original:  In this paper, we combine techniques from string processing (specifically, prefix-sorting) and automata theory (specifically, DFA minimization) to speed up solutions for this problem on languages described by finite automata.
Revised:  In this paper, we approach the problem by combining techniques from string processing (specifically, prefix-sorting) and automata theory (specifically, DFA minimization) to speed up solutions for this problem on languages described by finite automata.
Edit intent: clarity
Original:  String indexes allow solving efficiently a large number of problems, including counting and locating occurrences of a pattern in the indexed string.
Edit intent: coherence
Original:  In order to achieve this result we use the recent notion of Wheeler graph [Gagie et al., TCS 2017] , which extends naturally the concept of prefix sorting to labeled graphs .
Revised:  In order to achieve this result we use the recent notion of Wheeler graph [Gagie et al., TCS 2017] -which extends naturally the concept of prefix sorting to labeled graphs .
Edit intent: fluency
Original:  In this review we describe a common pipeline , thoroughly dissect the applied methods and highlight open questions for the individual steps.
Revised:  In this review we describe a common pipeline , thoroughly dissect these methods and highlight open questions for the individual steps.
Edit intent: clarity
Original:  An initial investigation of the biological target system and the desired components as well as the definition of design objectivesincluding the functional mechanism are fundamental prerequisites.
Revised:  Initially, it is essential to investigate the biological target system and the desired components as well as the definition of design objectivesincluding the functional mechanism are fundamental prerequisites.
Edit intent: coherence
Original:  It can be usually split into constrained sequence sampling, the formulation of an optimization problem and an in silico analysis step to narrow down the number of candidates with respect to secondary goals.
Revised:  This process can usually be split into constrained sequence sampling, the formulation of an optimization problem and an in silico analysis step to narrow down the number of candidates with respect to secondary goals.
Edit intent: clarity
Original:  It can be usually split into constrained sequence sampling, the formulation of an optimization problem and an in silico analysis step to narrow down the number of candidates with respect to secondary goals.
Revised:  It can be usually split into constrained sequence sampling, the formulation of an optimization problem and an in silico analysis to narrow down the number of candidates with respect to secondary goals.
Edit intent: clarity
Original:  Finally, experimental analysis  to check whether the defined design objectives are indeed met in the target environment and detailed characterization experiments are performed to improve the mechanistic models and detect missing design goals .
Revised:  Finally, experimental analysis is important to check whether the defined design objectives are indeed met in the target environment and detailed characterization experiments are performed to improve the mechanistic models and detect missing design goals .
Edit intent: coherence
Original:  Finally, experimental analysis  to check whether the defined design objectives are indeed met in the target environment and detailed characterization experiments are performed to improve the mechanistic models and detect missing design goals .
Revised:  Finally, experimental analysis to check whether the defined design objectives are indeed met in the target environment and detailed characterization experiments should be performed to improve the mechanistic models and detect missing design goals .
Edit intent: clarity