wanyu/IteraTeR_v2 huggingface dataset:
Original:  When the input polynomial has integer coefficients, our algorithm performs, up to poly-logarithmic factors, %DIFDELCMD < \widetilde{O}%%% _B(D\ell }   + D^4 + D^3 \tau) bit operations, where \tau is the maximum bitsize of the coefficients and 2^{ - \ell } } is the relative error of the terms in the decomposition.
Revised:  When the input polynomial has integer coefficients, our algorithm performs, up to poly-logarithmic factors, %DIFDELCMD < \widetilde{O}%%% _B(D\ell } (D + D^4 + D^3 \tau) bit operations, where \tau is the maximum bitsize of the coefficients and 2^{ - \ell } } is the relative error of the terms in the decomposition.
Edit intent: fluency
Original:  When the input polynomial has integer coefficients, our algorithm performs, up to poly-logarithmic factors, %DIFDELCMD < \widetilde{O}%%% _B(D\ell }   + D^4 + D^3 \tau) bit operations, where \tau is the maximum bitsize of the coefficients and 2^{ - \ell } } is the relative error of the terms in the decomposition.
Revised:  When the input polynomial has integer coefficients, our algorithm performs, up to poly-logarithmic factors, %DIFDELCMD < \widetilde{O}%%% _B(D\ell } \ell + D^4 + D^3 \tau) bit operations, where \tau is the maximum bitsize of the coefficients and 2^{ - \ell } } is the relative error of the terms in the decomposition.
Edit intent: fluency
Original:  When the input polynomial has integer coefficients, our algorithm performs, up to poly-logarithmic factors, %DIFDELCMD < \widetilde{O}%%% _B(D\ell }   + D^4 + D^3 \tau) bit operations, where \tau is the maximum bitsize of the coefficients and 2^{ - \ell } } is the relative error of the terms in the decomposition.
Revised:  When the input polynomial has integer coefficients, our algorithm performs, up to poly-logarithmic factors, %DIFDELCMD < \widetilde{O}%%% _B(D\ell } + D^4 + D^3 \tau) bit operations, where \tau is the maximum bitsize of the coefficients and 2^{ -- \ell } } is the relative error of the terms in the decomposition.
Edit intent: fluency
Original: In order to learn effective features from temporal sequences, the long short-term memory (LSTM) network is widely applied.
Revised: Attention is an important cognition process of humans, which helps humans concentrate on critical information during their perception and learning. However, although many machine learning models can remember information of data, they have no the attention mechanism. For example, the long short-term memory (LSTM) network is widely applied.
Edit intent: coherence
Original:  In this paper, we present a novel neural model , called long short-term attention (LSTA), which seamlessly merges the attention mechanism into  LSTM.
Revised:  In this paper, we present a novel model called long short-term attention (LSTA), which seamlessly merges the attention mechanism into LSTM.
Edit intent: clarity
Original:  In this paper, we present a novel neural model , called long short-term attention (LSTA), which seamlessly merges the attention mechanism into  LSTM.
Revised:  In this paper, we present a novel neural model , called long short-term attention (LSTA), which seamlessly integrates the attention mechanism into LSTM.
Edit intent: fluency
Original:  More than processing long short term sequences, it can distill effective and valuable information from the sequences with the attention mechanism.
Revised:  More than processing long short term dependencies, LSTA can focus on important information of the sequences with the attention mechanism.
Edit intent: clarity
Original:  Experiments show that LSTA achieves promising learning performance in various deep learning tasks.
Revised:  Extensive experiments demonstrate that LSTA outperforms LSTM and related models on the sequence learning tasks.
Edit intent: clarity
Original:  This random time can represent the death time of an agent or the default time of a firm, and in both cases \tau can not be seen before it occurs .
Revised:  This random time can represent the death time of an agent or the default time and the death time respectively .
Edit intent: clarity
Original: Identifying and explaining the structure of complex networks at the different scales has become an important problem across disciplines.
Revised: Identifying and explaining the structure of complex networks at different scales has become an important problem across disciplines.
Edit intent: fluency
Original:  However, empirical evidence increasingly suggests that characterizing a network with a unique pattern typology may be too simplistic, since a system can integrate properties from different organizations at each scale .
Revised:  However, empirical evidence increasingly suggests that characterizing a network with a unique pattern typology may be too simplistic, since a system can integrate properties from distinct organizations at different scales .
Edit intent: clarity
Original:  From the in-block nestedness perspective, we show that it provides a parsimonious transition between nested and modular networks, taking properties of both.
Revised:  Furthermore, we evince that in-block nestedness perspective, we show that it provides a parsimonious transition between nested and modular networks, taking properties of both.
Edit intent: coherence
Original:  From the in-block nestedness perspective, we show that it provides a parsimonious transition between nested and modular networks, taking properties of both.
Revised:  From the in-block nestedness provides a parsimonious transition between nested and modular networks, taking properties of both.
Edit intent: coherence
Original:  Beyond a merely theoretical exercise, understanding the boundaries that discriminate each architecture is fundamental, to the extent that modularity and nestedness are known to place heavy constraints to the stability of  dynamical processes, for example in ecological networks .
Revised:  Far from a mere theoretical exercise, understanding the boundaries that discriminate each architecture is fundamental, to the extent that modularity and nestedness are known to place heavy constraints to the stability of dynamical processes, for example in ecological networks .
Edit intent: clarity
Original:  Beyond a merely theoretical exercise, understanding the boundaries that discriminate each architecture is fundamental, to the extent that modularity and nestedness are known to place heavy constraints to the stability of  dynamical processes, for example in ecological networks .
Revised:  Beyond a merely theoretical exercise, understanding the boundaries that discriminate each architecture is fundamental, to the extent modularity and nestedness are known to place heavy constraints to the stability of dynamical processes, for example in ecological networks .
Edit intent: fluency
Original:  Beyond a merely theoretical exercise, understanding the boundaries that discriminate each architecture is fundamental, to the extent that modularity and nestedness are known to place heavy constraints to the stability of  dynamical processes, for example in ecological networks .
Revised:  Beyond a merely theoretical exercise, understanding the boundaries that discriminate each architecture is fundamental, to the extent that modularity and nestedness are known to place heavy constraints on the stability of dynamical processes, for example in ecological networks .
Edit intent: fluency
Original:  Beyond a merely theoretical exercise, understanding the boundaries that discriminate each architecture is fundamental, to the extent that modularity and nestedness are known to place heavy constraints to the stability of  dynamical processes, for example in ecological networks .
Revised:  Beyond a merely theoretical exercise, understanding the boundaries that discriminate each architecture is fundamental, to the extent that modularity and nestedness are known to place heavy constraints to the stability of several dynamical processes, for example in ecological networks .
Edit intent: clarity
Original:  Beyond a merely theoretical exercise, understanding the boundaries that discriminate each architecture is fundamental, to the extent that modularity and nestedness are known to place heavy constraints to the stability of  dynamical processes, for example in ecological networks .
Revised:  Beyond a merely theoretical exercise, understanding the boundaries that discriminate each architecture is fundamental, to the extent that modularity and nestedness are known to place heavy constraints to the stability of dynamical processes, specially in ecology .
Edit intent: clarity
Original: Recently Bravyi, Gosset and K\"onig (Science 2018) proved an unconditional separation between the computational powers of small-depth quantum and classical circuits for a relation in the worst-case setting , and left the existence of a similar separation in the average-case setting, which would give a much stronger evidence of the superiority of small-depth quantum computation, as an open problem.
Revised: Recently Bravyi, Gosset and K\"onig (Science 2018) proved an unconditional separation between the computational powers of small-depth quantum and classical circuits for a relation in the worst-case setting and left the existence of a similar separation in the average-case setting, which would give a much stronger evidence of the superiority of small-depth quantum computation, as an open problem.
Edit intent: fluency
Original:  In this paper we solve this problem: we construct a computational task that can be solved on all inputs by a quantum circuit of constant depth with bounded-fanin gates (a `shallow' quantum circuit) and show that any classical circuit with bounded-fanin gates solving this problem with high probability on a fraction 1-\delta of the inputs , for some constant \delta>0, must have logarithmic depth.
Revised:  In this paper we solve this problem: we construct a computational task that can be solved on all inputs by a quantum circuit of constant depth with bounded-fanin gates (a `shallow' quantum circuit) and show that any classical circuit with bounded-fanin gates solving this problem with high probability on a fraction 1-\delta of the inputs must have logarithmic depth.
Edit intent: coherence
Original:  The same construction also gives a distribution that can be sampled exactly by shallow quantum circuits, but such that any classical circuit approximating it, even with constant additive error, must have logarithmic depth.
Edit intent: coherence
Original:  A similar result has been very recently (and independently) obtained by Coudron, Stark and Vidick (arXiv:1810.04233)  .
Revised:  Similar results have been very recently (and independently) obtained by Coudron, Stark and Vidick (arXiv:1810.04233) .
Edit intent: clarity
Original: Recently Bravyi, Gosset and K\"onig (Science 2018) proved an unconditional separation between the computational powers of small-depth quantum and classical circuits for a relation in the worst-case setting and left the existence of a similar separation in the average-case setting , which would give a much stronger evidence of the superiority of small-depth quantum computation , as an open problem.
Revised: Recently Bravyi, Gosset and K\"onig (Science 2018) proved an unconditional separation between the computational powers of small-depth quantum and classical circuits for a relation . In this paper we show a similar separation in the average-case setting , which would give a much stronger evidence of the superiority of small-depth quantum computation , as an open problem.
Edit intent: clarity
Original: Recently Bravyi, Gosset and K\"onig (Science 2018) proved an unconditional separation between the computational powers of small-depth quantum and classical circuits for a relation in the worst-case setting and left the existence of a similar separation in the average-case setting , which would give a much stronger evidence of the superiority of small-depth quantum computation , as an open problem.
Revised: Recently Bravyi, Gosset and K\"onig (Science 2018) proved an unconditional separation between the computational powers of small-depth quantum and classical circuits for a relation in the worst-case setting and left the existence of a similar separation in the average-case setting that gives a stronger evidence of the superiority of small-depth quantum computation , as an open problem.
Edit intent: clarity
Original:  In this paper we solve this problem : we construct a computational task that can be solved on all inputs by a quantum circuit of constant depth with bounded-fanin gates (a `shallow' quantum circuit) and show that any classical circuit with bounded-fanin gates solving this problem on a non-negligible fraction of the inputs must have logarithmic depth.
Revised:  In this paper we solve this problem : we construct a computational task that can be solved on all inputs by a quantum circuit of constant depth with bounded-fanin gates (a "shallow" quantum circuit) and show that any classical circuit with bounded-fanin gates solving this problem on a non-negligible fraction of the inputs must have logarithmic depth.
Edit intent: fluency
Original:  In this paper we show a similar separation in the average-case setting that gives a stronger evidence of the superiority of small-depth quantum computation: we construct a computational task that can be solved on all inputs by a quantum circuit of constant depth with bounded-fanin gates (a "shallow" quantum circuit) and show that any classical circuit with bounded-fanin gates solving this problem on a non-negligible fraction of the inputs must have logarithmic depth.
Revised:  In this paper we show a similar separation in the average-case setting that gives stronger evidence of the superiority of small-depth quantum computation: we construct a computational task that can be solved on all inputs by a quantum circuit of constant depth with bounded-fanin gates (a "shallow" quantum circuit) and show that any classical circuit with bounded-fanin gates solving this problem on a non-negligible fraction of the inputs must have logarithmic depth.
Edit intent: fluency
Original:  Our results are obtained by introducing a technique to create quantum states exhibiting global quantum correlations from any graph, via a construction that we call the extended graph . Similar results have been very recently (and independently) obtained by Coudron, Stark and Vidick (arXiv:1810.04233), and Bene Watts, Kothari, Schaeffer and Tal  .
Revised:  Our results are obtained by introducing a technique to create quantum states exhibiting global quantum correlations from any graph, via a construction that we call the extended graph . Similar results have been very recently (and independently) obtained by Coudron, Stark and Vidick (arXiv:1810.04233), and Bene Watts, Kothari, Schaeffer and Tal .
Edit intent: fluency
Original:  This is used to prove that local minima of the  loss function in this open set are isolated, and that every critical point below this error threshold is a local minimum, partially addressing an open problem given at the Conference on Learning Theory (COLT) 2015.
Revised:  This is used to prove that local minima of the loss function in this set are isolated, and that every critical point below this error threshold is a local minimum, partially addressing an open problem given at the Conference on Learning Theory (COLT) 2015.
Edit intent: fluency
Original:  This is used to prove that local minima of the  loss function in this open set are isolated, and that every critical point below this error threshold is a local minimum, partially addressing an open problem given at the Conference on Learning Theory (COLT) 2015.
Revised:  This is used to prove that local minima of the loss function in this open set are isolated, and that every critical point in this set is a local minimum, partially addressing an open problem given at the Conference on Learning Theory (COLT) 2015.
Edit intent: clarity
Original:  We also include an experimental section where we validate our theoretical work by showing that the regularized loss function is almost always piecewise strongly convex when restricted to stochastic gradient descent trajectories for three standard image classification problems.
Revised:  We also include an experimental section where we validate our theoretical work and show that the regularized loss function is almost always piecewise strongly convex when restricted to stochastic gradient descent trajectories for three standard image classification problems.
Edit intent: clarity
Original: For a connected graph G we call a set \mathcal{F a spanning tree factoring of G if it contains all spanning trees of G. A subset S\subseteq V(G) }  is a simultaneous dominating set of G if it is a dominating set in every spanning tree in \mathcal{F .
Revised:  a spanning tree factoring of G if it contains all spanning trees of G. A subset S\subseteq V(G) } is a simultaneous dominating set of G if it is a dominating set in every spanning tree in \mathcal{F .
Edit intent: clarity
Original: For a connected graph G we call a set \mathcal{F a spanning tree factoring of G if it contains all spanning trees of G. A subset S\subseteq V(G) }  is a simultaneous dominating set of G if it is a dominating set in every spanning tree in \mathcal{F .
Revised: For a connected graph G we call a set \mathcal{F a spanning tree factoring of G if it contains all spanning trees of G. A subset S\subseteq V(G) } is a simultaneous dominating set for spanning trees if it is a dominating set in every spanning tree in \mathcal{F .
Edit intent: clarity
Original: For a connected graph G we call a set \mathcal{F a spanning tree factoring of G if it contains all spanning trees of G. A subset S\subseteq V(G) }  is a simultaneous dominating set of G if it is a dominating set in every spanning tree in \mathcal{F .
Revised: For a connected graph G we call a set \mathcal{F a spanning tree factoring of G if it contains all spanning trees of G. A subset S\subseteq V(G) } is a simultaneous dominating set of G if it is a dominating set in every spanning tree of the graph .
Edit intent: clarity
Original:  We consider the problem of finding a minimum size simultaneous dominating set for spanning tree factorings .
Revised:  We consider the problem of finding a minimum size simultaneous dominating set for spanning trees .
Edit intent: clarity
Original: A subset of the vertices of a graph is a simultaneous dominating set for spanning trees if it is a dominating set in every spanning tree of the graph.
Revised: We investigate the problem of simultaneously dominating all spanning trees of a given graph.
Edit intent: clarity
Original:  We present an exact algorithm to solve this problem and show how to solve it in polynomial time on some graph classeslike bipartite or chordal graphs.
Revised:  We present an exact algorithm to solve this problem and show how to solve it in polynomial time on several graph classes, such as bipartite or chordal graphs.
Edit intent: clarity
Original:  Moreover, we derive a 2-approximation algorithm for this problem .
Revised:  Moreover, we derive a 2-approximation algorithm for finding a minimum simultaneous dominating set .
Edit intent: clarity
Original:  The proof relies on some dynamic programming algorithms, using transfer matrices in (min,+)-algebra  We also apply the method to solve the Roman domination problem on grid graphs.
Revised:  The proof relies on some dynamic programming algorithms, using transfer matrices in (min,+)-algebra . We also apply the method to solve the Roman domination problem on grid graphs.
Edit intent: fluency
Original: We propose a neural field model of color perception in context , for the visual area V1 in the cortex.
Revised: We propose a neural field model of color perception with spatial context for the visual area V1 in the cortex.
Edit intent: clarity
Original: We propose a neural field model of color perception in context , for the visual area V1 in the cortex.
Revised: We propose a neural field model of color perception in context , for the visual area V1 of the cortex.
Edit intent: clarity
Original:  This model reconciles into a common framework two opposing perceptual phenomena,  simultaneous contrast and chromatic assimilation.
Revised:  Our framework reconciles two opposing perceptual phenomena, simultaneous contrast and chromatic assimilation.
Edit intent: clarity
Original:  This model reconciles into a common framework two opposing perceptual phenomena,  simultaneous contrast and chromatic assimilation.
Revised:  This model reconciles into a common framework two opposing perceptual phenomena, known as simultaneous contrast and chromatic assimilation.
Edit intent: clarity
Original:  At some point in an image, the color perceptually seems more similar to that of the adjacent locations , while being more dissimilar from that of remote neighbors.
Revised:  At some point in an image, the color seems perceptually more similar to that of the adjacent locations , while being more dissimilar from that of remote neighbors.
Edit intent: fluency
Original:  At some point in an image, the color perceptually seems more similar to that of the adjacent locations , while being more dissimilar from that of remote neighbors.
Revised:  At some point in an image, the color perceptually seems more similar to that of adjacent neighbors , while being more dissimilar from that of remote neighbors.
Edit intent: clarity
Original:  Alongside this neural field model, we describe the search for a color match in asymmetric matching experiments as a mathematical projector .
Revised:  Alongside this neural field model, we describe the search for a color match in asymmetric matching experiments as a mathematical projection on color sensations .
Edit intent: clarity
Original:  We validate it by fitting the parameters of the model to data from (Monnier and Shevell, 2004) and (Monnier, 2008) and our own data .
Revised:  We validate our color neural field alongside this color matching framework, by performing a multi-parameter regression to data produced by psychophysicists and ourselves .
Edit intent: clarity
Original:  All the results show that we are able to explain the nonlinear behavior of the observed shifts along one or two dimensions in color space, which cannot be done using a simple linear model.
Revised:  All the results show that we are able to explain the nonlinear behavior of shifts observed along one or two dimensions in color space, which cannot be done using a simple linear model.
Edit intent: fluency
Original: Paradoxically, bibliometric indicators (i.e., publications and citation counts) are  both widely used and widely criticized in research evaluation.
Revised: When scientists study the phenomena they are interested in, they apply sound methods and base their work on theoretical considerations. In contrast, when the fruits of their research is being evaluated, basic scientific standards do not seem to matter. Instead, simplistic bibliometric indicators (i.e., publications and citation counts) are both widely used and widely criticized in research evaluation.
Edit intent: coherence
Original: Paradoxically, bibliometric indicators (i.e., publications and citation counts) are  both widely used and widely criticized in research evaluation.
Revised: Paradoxically, bibliometric indicators (i.e., publications and citation counts) are , paradoxically, both widely used and widely criticized in research evaluation.
Edit intent: coherence
Original:  In this paper, we outline such a framework - the fast-and-frugal heuristics research framework developed by Gigerenzer et al. 1%DIFDELCMD < ] %%% - and discuss its application to evaluative bibliometrics.
Revised:  In this paper, we outline such a framework - the fast-and-frugal heuristics research framework developed by Gigerenzer et al. %DIFDELCMD < ] %%% - and discuss its application to evaluative bibliometrics.
Edit intent: fluency
Original:  In this paper, we outline such a framework - the fast-and-frugal heuristics research framework developed by Gigerenzer et al. 1%DIFDELCMD < ] %%% - and discuss its application to evaluative bibliometrics.
Revised:  In this paper, we outline such a framework - the fast-and-frugal heuristics research framework developed by Gigerenzer et al. 1%DIFDELCMD < ] %%% .
Edit intent: coherence