wanyu/IteraTeR_full_sent huggingface dataset:
Original:  The analogy with respect to the visual system structure is established, emerging directly from the architecture of the net .
Revised:  The analogy with respect to the visual system structure is established, emerging directly from the architecture of the neural network. A proof of rotation invariance of the first layer is given on a fixed LGN-CNN architecture and the computational results are shown. Thus, contrast invariance capability of the LGN-CNN is investigated and a comparison between the Retinex effects of the first layer of LGN-CNN and the Retinex effects of a LoG is provided on different images. A statistical study is done on the filters of the second convolutional layer with respect to biological data .
Edit intent: meaning-changed
Original: The crossing number cr(G) of a graph G is the minimum number of crossings over all possible drawings of G in the plane. Analogously, the k-planar crossing number of G, denoted by cr_{k edges of G in k disjoint planes.
Revised: The crossing number cr(G) of a graph G is the minimum number of crossings over all possible drawings of the edges of G in k disjoint planes.
Edit intent: clarity
Original:  In particular, for the case of k=2, we improve the current best lower bounds on biplanar crossing numbers by a factor of 1.37 for complete graphs, and by a factor of 1.34 for complete bipartite graphs.
Revised:  In particular, we prove that the biplanar crossing number of complete bipartite graphs can be approximated to within a factor of 1.37 for complete graphs, and by a factor of 1.34 for complete bipartite graphs.
Edit intent: clarity
Original:  In particular, for the case of k=2, we improve the current best lower bounds on biplanar crossing numbers by a factor of 1.37 for complete graphs, and by a factor of 1.34 for complete bipartite graphs.
Revised:  In particular, for the case of k=2, we improve the current best lower bounds on biplanar crossing numbers by a factor of 3, improving over the best previously known approximation factor of 4.03. For complete graphs, and by a factor of 1.34 for complete bipartite graphs.
Edit intent: meaning-changed
Original:  In particular, for the case of k=2, we improve the current best lower bounds on biplanar crossing numbers by a factor of 1.37 for complete graphs, and by a factor of 1.34 for complete bipartite graphs. We extend our results to the k-planar crossing number of complete (bipartite ) graphs, for any positive integer k \geq 2.
Revised:  In particular, for the case of k=2, we improve the current best lower bounds on biplanar crossing numbers by a factor of 1.37 for complete graphs, we provide a new approximation factor of 3.17, improving over the best previous factor of 4.34. We provide similar improved approximation factors for the k-planar crossing number of complete (bipartite ) graphs, for any positive integer k \geq 2.
Edit intent: meaning-changed
Original:  We extend our results to the k-planar crossing number of complete (bipartite ) graphs, for any positive integer k \geq 2. To better understand the relation between crossing numbers and biplanar crossing numbers, we pose a new problem of finding the largest crossing number that implies biplanarity.
Revised:  We extend our results to the k-planar crossing number of complete (bipartite ) graphs, for any positive integer k . We also investigate the relation between crossing numbers and biplanar crossing numbers, we pose a new problem of finding the largest crossing number that implies biplanarity.
Edit intent: coherence
Original:  To better understand the relation between crossing numbers and biplanar crossing numbers, we pose a new problem of finding the largest crossing number that implies biplanarity. In particular, we prove that for every graph G, cr(G) \leq 10 implies cr_{2
Revised:  To better understand the relation between crossing numbers and biplanar crossing number of general graphs in more depth, and prove that any graph with a crossing number of at most 10 implies cr_{2
Edit intent: meaning-changed
Original: To transform a single-celled zygote into an adult URLanism, development employs three basic processes --- asymmetric cell division, signaling and gene regulation . These three processes can be combined in a multitude of ways , thus generating the huge diversity of plant and animal forms we see today.
Revised: To transform a single-celled zygote into an adult URLanism, development employs three basic processes --- asymmetric cell division, signaling and gene regulation --- in a multitude of ways , thus generating the huge diversity of plant and animal forms we see today.
Edit intent: coherence
Original:  These three processes can be combined in a multitude of ways , thus generating the huge diversity of plant and animal forms we see today. The wealth of possible developmental schemes created by this combinatorial explosion is hard to survey and understand. Here, with a generative Boolean model , we demonstrate and systematically chart the extent of diversity that development can potentially produce.
Revised:  These three processes can be combined in a multitude of ways to create an overwhelming diversity of multicellular life-forms. Here , we demonstrate and systematically chart the extent of diversity that development can potentially produce.
Edit intent: clarity
Original:   Additionally, in line with the hypothesis that whole body regeneration is an epiphenomenon of development, a majority of URLanisms generated by our model can regenerate using pluripotent cells  .
Revised:  Instead, they are more likely to be directed acyclic graphs, with multiple lineages converging on the same terminal cell-type. Additionally, in line with the hypothesis that whole body regeneration is an epiphenomenon of development, a majority of URLanisms generated by our model can regenerate using pluripotent cells .
Edit intent: meaning-changed
Original:   Additionally, in line with the hypothesis that whole body regeneration is an epiphenomenon of development, a majority of URLanisms generated by our model can regenerate using pluripotent cells  .
Revised:  Additionally, in line with the hypothesis that whole body regeneration is an epiphenomenon of development, a majority of URLanisms generated by our model can regenerate using pluripotent cells . The generative framework is modular and flexible, and can be adapted to test additional hypotheses about general features of development .
Edit intent: meaning-changed
Original:  This is not true in general and in many settings, the probability of purchase may decrease if we add more products to the assortment, referred to as the %DIFDELCMD < {\em %%% choice overload .
Revised:  This is not true in general and in many settings, the probability of purchase may decrease if we add more products to the assortment, referred to as the %DIFDELCMD < {\em %%% choice overload .
Edit intent: fluency
Original:  In particular, we handle dynamic preferences and the choice overload phenomenon using a %DIFDELCMD < {\em %%% Markovian comparison model that is a generalization of the Markovian substitution framework of Blanchet et al.
Revised:  In particular, we handle dynamic preferences and the choice overload phenomenon using a %DIFDELCMD < {\em %%% Markovian comparison model that is a generalization of the Markovian substitution framework of Blanchet et al.
Edit intent: fluency
Original:  Firms face a choice between secrecy, which protects existing intellectual property, and openness, which facilitates social learning . These decisions determine interaction rates between firms, and these interaction rates enter our model as link probabilities in a resulting learning network.
Revised:  Firms face a choice between secrecy, which protects existing intellectual property, and openness, which facilitates learning from others. Their decisions determine interaction rates between firms, and these interaction rates enter our model as link probabilities in a resulting learning network.
Edit intent: clarity
Original:  However,  many models of social interactions do not satisfy this assumption. This paper proposes a substantially weaker model of "approximate neighborhood interference" (ANI) , under which treatments assigned to alters further from the ego have a smaller, but potentially nonzero, impact on the ego's response.
Revised:  However, many models of social interactions . We propose a substantially weaker model of "approximate neighborhood interference" (ANI) , under which treatments assigned to alters further from the ego have a smaller, but potentially nonzero, impact on the ego's response.
Edit intent: clarity
Original:  This paper proposes a substantially weaker model of "approximate neighborhood interference" (ANI) , under which treatments assigned to alters further from the ego have a smaller, but potentially nonzero, impact on the ego's response.
Revised:  This paper proposes a substantially weaker model of "approximate neighborhood interference" (ANI) under which treatments assigned to alters further from the ego have a smaller, but potentially nonzero, impact on the ego's response.
Edit intent: fluency
Original:  This paper proposes a substantially weaker model of "approximate neighborhood interference" (ANI) , under which treatments assigned to alters further from the ego have a smaller, but potentially nonzero, impact on the ego's response.
Revised:  This paper proposes a substantially weaker model of "approximate neighborhood interference" (ANI) , under which treatments assigned to alters further from the ego have smaller, but potentially nonzero, impact on the ego's response.
Edit intent: fluency
Original:  This paper proposes a substantially weaker model of "approximate neighborhood interference" (ANI) , under which treatments assigned to alters further from the ego have a smaller, but potentially nonzero, impact on the ego's response.
Revised:  This paper proposes a substantially weaker model of "approximate neighborhood interference" (ANI) , under which treatments assigned to alters further from the ego have a smaller, but potentially nonzero, effects on the ego's response.
Edit intent: fluency
Original:  We also prove that, under ANI  , standard inverse-probability weighting estimators can consistently estimate useful exposure effects and are asymptotically normal under asymptotics taking the network size large.
Revised:  We also prove that, under ANI and restrictions on the network topology , standard inverse-probability weighting estimators can consistently estimate useful exposure effects and are asymptotically normal under asymptotics taking the network size large.
Edit intent: meaning-changed
Original:  First, we show that the Ranked Pairs and Schulze rules have distortion \Theta(\sqrt(n)). Second, we give a fairly simple proof of a strong generalization of the upper bound of 5 on the distortion of Copeland, to social choice rules with short paths from the winning candidate to the optimal candidate in generalized weak preference graphs.
Revised:  First, we give a fairly simple proof of a strong generalization of the upper bound of 5 on the distortion of Copeland, to social choice rules with short paths from the winning candidate to the optimal candidate in generalized weak preference graphs.
Edit intent: coherence
Original:  Current methods, branded as geometric matrix completion, augment classical rank regularization techniques by incorporating geometric information into the solution. This information is usually provided as graphs encoding relations between rows/columns. In this work we propose a simple spectral approach for solving the matrix completion problem, via the framework of functional maps. We introduce the zoomout loss, a multiresolution spectral geometric loss inspired by recent advances in shape correspondence, whose minimization leads to state-of-the-art results on various recommender systems datasets. Surprisingly, for some datasets we were able to achieve comparable results even without incorporating geometric information. This puts into question both the quality of such information and current methods' ability to use it in a meaningful and efficient way .
Revised:  Recent works have established that gradient descent applied to a DMF model induces an implicit regularization on the rank of the recovered matrix. Despite these promising theoretical results, empirical evaluation of vanilla DMF on real benchmarks exhibits poor reconstructions which we attribute to the extremely low number of samples available. We propose an explicit spectral regularization scheme that is able to make DMF models competitive on real benchmarks, while still maintaining the implicit regularization induced by gradient descent, thus enjoying the best of both worlds .
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Original: Deep Matrix Factorization (DMF) is an emerging approach to the problem of reconstructing a matrix from a subset of its entries . Recent works have established that gradient descent applied to a DMF model induces an implicit regularization on the rank of the recovered matrix.
Revised: Deep Matrix Factorization (DMF) is an emerging approach to the problem of matrix completion . Recent works have established that gradient descent applied to a DMF model induces an implicit regularization on the rank of the recovered matrix.
Edit intent: clarity
Original:  Despite these promising theoretical results, empirical evaluation of vanilla DMF on real benchmarks exhibits poor reconstructions which we attribute to the extremely low number of samples available. We propose an explicit spectral regularization scheme that is able to make DMF models competitive on real benchmarks, while still maintaining the implicit regularization induced by gradient descent, thus enjoying the best of both worlds .
Revised:  In this work we interpret the DMF model through the lens of spectral geometry. This allows us to incorporate explicit regularization without breaking the DMF structure, thus enjoying the best of both worlds. In particular, we focus on matrix completion problems with underlying geometric or topological relations between the rows and/or columns. Such relations are prevalent in matrix completion problems that arise in many applications, such as recommender systems and drug-target interaction. Our contributions enable DMF models to exploit these relations, and make them competitive on real benchmarks, while still maintaining the implicit regularization induced by gradient descent, thus enjoying the best of both worlds .
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Original: Millimeter-wave radar, in marriage with virtual massive multiple-input multiple-output (MIMO) system, provides great promises to super-resolution environment sensing and target detection in unmanned ground/aerial vehicle (UGA/UAV).
Revised: Massive multiple-input multiple-output (MIMO) system, provides great promises to super-resolution environment sensing and target detection in unmanned ground/aerial vehicle (UGA/UAV).
Edit intent: clarity
Original: Millimeter-wave radar, in marriage with virtual massive multiple-input multiple-output (MIMO) system, provides great promises to super-resolution environment sensing and target detection in unmanned ground/aerial vehicle (UGA/UAV).
Revised: Millimeter-wave radar, in marriage with virtual massive multiple-input multiple-output (MIMO) radar, assisted by millimeter-wave band virtual MIMO techniques, provides great promises to super-resolution environment sensing and target detection in unmanned ground/aerial vehicle (UGA/UAV).
Edit intent: meaning-changed
Original: Millimeter-wave radar, in marriage with virtual massive multiple-input multiple-output (MIMO) system, provides great promises to super-resolution environment sensing and target detection in unmanned ground/aerial vehicle (UGA/UAV).
Revised: Millimeter-wave radar, in marriage with virtual massive multiple-input multiple-output (MIMO) system, provides great promises to the high-resolution automotive sensing and target detection in unmanned ground/aerial vehicle (UGA/UAV).
Edit intent: clarity
Original: Millimeter-wave radar, in marriage with virtual massive multiple-input multiple-output (MIMO) system, provides great promises to super-resolution environment sensing and target detection in unmanned ground/aerial vehicle (UGA/UAV).
Revised: Millimeter-wave radar, in marriage with virtual massive multiple-input multiple-output (MIMO) system, provides great promises to super-resolution environment sensing and target detection in unmanned ground/aerial vehicles (UGA/UAV).
Edit intent: fluency
Original:  In this work , we propose two efficient approximate algorithms to significantly accelerate the high-resolution subspace algorithm. In particular, our fast MUST algorithms speed up the expensive signal subspace identification step using the randomized low-rank approximations.
Revised:  In this work , we propose two efficient approximate algorithms to significantly accelerate the high-resolution estimation of angle of arrival (AoA) information. By leveraging randomized low-rank approximation, our fast-MUSIC approaches, relying on random sampling and projection techniques, would speed up the expensive signal subspace identification step using the randomized low-rank approximations.
Edit intent: meaning-changed
Original:  In particular, our fast MUST algorithms speed up the expensive signal subspace identification step using the randomized low-rank approximations. We also establish theoretical bounds to guarantee the quality of approximation. Specifically, we show that, in the case of high signal-to-noise ratio, the pseudo-spectrum produced by our algorithms are very close to the exact MUSIC.
Revised:  In particular, our fast MUST algorithms speed up the subspace computation by orders of magnitude. At the same time, we establish the theoretical bounds of our proposed approaches, which ensure the accuracy of approximated pseudo-spectrum. As shown, in the case of high signal-to-noise ratio, the pseudo-spectrum produced by our algorithms are very close to the exact MUSIC.
Edit intent: clarity
Original:  Our theoretical analysis is original, which does not simply follow from any existing work. Our comprehensive empirical study shows that our algorithms are tremendously faster than MUSIC, while their target detection accuracies in massive MIMO radar are almost as good as MUSIC.
Revised:  Comprehensive numerical study demonstrates that our new methods are tremendously faster than MUSIC, while their target detection accuracies in massive MIMO radar are almost as good as MUSIC.
Edit intent: clarity
Original:  The unsupervised learning can then be decomposed into two interwoven steps: a maximization step is carried out as a gradient ascent of the lower-bound on the data log-likelihood,  and an expectation step is carried out as a message passing procedure on an equivalent or dual neural network whose parameter is specified by the variational parameter of the weight distribution.
Revised:  The unsupervised learning can then be decomposed into two intertwined steps: a maximization step is carried out as a gradient ascent of the lower-bound on the data log-likelihood, and an expectation step is carried out as a message passing procedure on an equivalent or dual neural network whose parameter is specified by the variational parameter of the weight distribution.
Edit intent: fluency
Original:  The unsupervised learning can then be decomposed into two interwoven steps: a maximization step is carried out as a gradient ascent of the lower-bound on the data log-likelihood,  and an expectation step is carried out as a message passing procedure on an equivalent or dual neural network whose parameter is specified by the variational parameter of the weight distribution.
Revised:  The unsupervised learning can then be decomposed into two interwoven steps: a maximization step is carried out as a gradient ascent of the lower-bound on the data log-likelihood, in which the synaptic weight distribution is determined by updating variational parameters, and an expectation step is carried out as a message passing procedure on an equivalent or dual neural network whose parameter is specified by the variational parameter of the weight distribution.
Edit intent: meaning-changed
Original:  The unsupervised learning can then be decomposed into two interwoven steps: a maximization step is carried out as a gradient ascent of the lower-bound on the data log-likelihood,  and an expectation step is carried out as a message passing procedure on an equivalent or dual neural network whose parameter is specified by the variational parameter of the weight distribution.
Revised:  The unsupervised learning can then be decomposed into two interwoven steps: a maximization step is carried out as a gradient ascent of the lower-bound on the data log-likelihood, and an expectation step is carried out as a message passing procedure on an equivalent or dual neural network whose parameter is specified by the variational parameters of the weight distribution.
Edit intent: fluency
Original: Given a point set P , are k closed convex polygons sufficient to partition the convex hull of P , such that the interior of a convex set contains no point in P? What if the vertices of these polygons are constrained to be points of P ? We show that the first decision problem is NP-hard, and the second NP-complete } .
Revised: Given a point set P , are k closed convex polygons sufficient to partition the convex hull of P of n points in the plane, draw a plane graph G on P, with positive minimum degree, such that G partitions the convex hull of P into a minimum number of convex faces. We show that the first decision problem is NP-hard, and the second NP-complete } .
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Original:  What if the vertices of these polygons are constrained to be points of P ? We show that the first decision problem is NP-hard, and the second NP-complete } .
Revised:  What if the vertices of these polygons are constrained to be points of P ? We show that the first decision problem is NP-hard, and the second NP-complete }log n)-approximation algorithm running in quadratic time. The latter result is obtained by relating the problem to another geometric problem: Given a set of points P, cover P with a minimum number of lines. A constant-factor approximation algorithm was shown for Minimum Convex Partition by Knauer and Spillner, for point sets where no three points are on a line (SWAT 2006). This restriction is crucial for the algorithm to work. The complexity of the problem under this restriction remains open .
Edit intent: meaning-changed
Original:  We use dynamical renormalization group approach to study a stochastic model for chemotactic particles in which we introduce polarization effects in chemotaxis.
Revised:  We develop a systematic coarse-graining scheme using which we can construct a general theoretical framework to study many-body effects in chemotactic populations. The framework unveils a polarization-induced coupling term, which originates from quorum effects and can compete with the chemotactic drift term. We use the dynamical renormalization group approach to study a stochastic model for chemotactic particles in which we introduce polarization effects in chemotaxis.
Edit intent: meaning-changed
Original:  A generically observed mechanism that drives URLanization is interaction among the individual elements---which may represent cells, bacteria, or even enzymes---via chemical signals. We develop a systematic coarse-graining scheme using which we can construct a general theoretical framework to study many-body effects in chemotactic populations. The framework unveils a polarization-induced coupling term , which originates from quorum effects and can compete with the chemotactic drift term.
Revised:  A generically observed mechanism that drives URLanization is interaction among the individual elements---which may represent cells, bacteria, or even enzymes. Here we propose a novel mechanism for such interactions, in the context of chemotaxis , which originates from quorum effects and can compete with the chemotactic drift term.
Edit intent: clarity