wanyu/IteraTeR_v2 huggingface dataset:
Original:  The compartment limits the diffusion of the intermediate compounds, thereby also maintaining the genotype-phenotype linkage enabling natural selection.
Revised:  The compartment limits the diffusion of the intermediate compounds, thereby also maintaining the genotype-phenotype linkage , is a critical function of compartments in natural selection.
Edit intent: coherence
Original:  In most cases however, genotypic variants are distributed randomly among the hosts .
Revised:  In most cases however, individual replicating elements do not distribute systematically among the hosts .
Edit intent: clarity
Original:  More than one variant may thus occupy each compartment , blurring the genotype-phenotype linkage : how does this affect the effectiveness of natural selection ?
Revised:  More than one variant may thus occupy some compartments , blurring the genotype-phenotype linkage : how does this affect the effectiveness of natural selection ?
Edit intent: clarity
Original:  More than one variant may thus occupy each compartment , blurring the genotype-phenotype linkage : how does this affect the effectiveness of natural selection ?
Revised:  More than one variant may thus occupy each compartment , blurring the genotype-phenotype linkage and affecting the effectiveness of natural selection ?
Edit intent: clarity
Original:  More than one variant may thus occupy each compartment , blurring the genotype-phenotype linkage : how does this affect the effectiveness of natural selection ?
Revised:  More than one variant may thus occupy each compartment , blurring the genotype-phenotype linkage : how does this affect the effectiveness of natural selection .
Edit intent: fluency
Original:  and thereby allows a natural generalization to arbitrary p,q, r , 1 %DIFDELCMD < \le %%% p, q,r%DIFDELCMD < \le %%% \infty.
Revised:  and thereby allows a natural generalization to arbitrary p,q, r , 1 %DIFDELCMD < \le %%% %DIFDELCMD < \le %%% \infty.
Edit intent: fluency
Original: %DIFDELCMD < \[ %DIFDELCMD < \lVert\mu_{l,m,n}\rVert_{p,q,r}=\max_{X,Y,M\neq0}\frac{|\operatorname{tr}(XMY)|}{\|X\|_{p,q}\|Y\|_{q,r}\|M\|_{r,p}}\leq %DIFDELCMD < K_G \cdot l^{|1/q-1/2|} \cdot m^{1-1/p} \cdot n^{1/r}, \]%%%  \[ \lVert\mu_{l,m,n}\rVert_{p,q,r}=\max_{X,Y,M\neq0}\frac{|\operatorname{tr}(XMY)|}{\|X\|_{p,q}\|Y\|_{q,r}\|M\|_{r,p}}, \] and conjecture that Grothendieck's inequality is unique:
Revised: %DIFDELCMD < \[ %DIFDELCMD < \lVert\mu_{l,m,n}\rVert_{p,q,r}=\max_{X,Y,M\neq0}\frac{|\operatorname{tr}(XMY)|}{\|X\|_{p,q}\|Y\|_{q,r}\|M\|_{r,p}}\leq %DIFDELCMD < K_G \cdot l^{|1/q-1/2|} \cdot m^{1-1/p} \cdot n^{1/r}, \]%%% ,\[ \lVert\mu_{l,m,n}\rVert_{p,q,r}=\max_{X,Y,M\neq0}\frac{|\operatorname{tr}(XMY)|}{\|X\|_{p,q}\|Y\|_{q,r}\|M\|_{r,p}}, \] and conjecture that Grothendieck's inequality is unique:
Edit intent: fluency
Original:  We establish two-thirds of this conjecture: uniform boundedness of%DIFDELCMD < \lVert%%% \mu_{l,m,n}%DIFDELCMD < \rVert%%% _{p,q,r l,m,n necessarily implies that \min \{p,q,r\}=1 and \max \{p,q,r\}=\infty .
Revised:  We establish two-thirds of this conjecture: uniform boundedness of%DIFDELCMD < \lVert%%% }%DIFDELCMD < \rVert%%% _{p,q,r l,m,n necessarily implies that \min \{p,q,r\}=1 and \max \{p,q,r\}=\infty .
Edit intent: clarity
Original:  We establish two-thirds of this conjecture: uniform boundedness of%DIFDELCMD < \lVert%%% \mu_{l,m,n}%DIFDELCMD < \rVert%%% _{p,q,r l,m,n necessarily implies that \min \{p,q,r\}=1 and \max \{p,q,r\}=\infty .
Revised:  We establish two-thirds of this conjecture: uniform boundedness of%DIFDELCMD < \lVert%%% \mu_{l,m,n}%DIFDELCMD < \rVert%%% independent of l,m,n necessarily implies that \min \{p,q,r\}=1 and \max \{p,q,r\}=\infty .
Edit intent: clarity
Original:  In this paper, we propose a Differentiable Inductive Logic framework (%DIFDELCMD < \partialILP%%% ) , which can not only solve tasks which traditional ILP systems are suited for, but shows a robustness to noise and error in the training data which ILP cannot cope with.
Revised:  In this paper, we propose a Differentiable Inductive Logic framework %DIFDELCMD < \partialILP%%% ) , which can not only solve tasks which traditional ILP systems are suited for, but shows a robustness to noise and error in the training data which ILP cannot cope with.
Edit intent: fluency
Original:  In this paper, we propose a Differentiable Inductive Logic framework (%DIFDELCMD < \partialILP%%% ) , which can not only solve tasks which traditional ILP systems are suited for, but shows a robustness to noise and error in the training data which ILP cannot cope with.
Revised:  In this paper, we propose a Differentiable Inductive Logic framework (%DIFDELCMD < \partialILP%%% , which can not only solve tasks which traditional ILP systems are suited for, but shows a robustness to noise and error in the training data which ILP cannot cope with.
Edit intent: fluency
Original: Background: Gene co-expression network analyses have become a central approach for the systems-level analysis of biological data.
Revised: Network analyses, such as of gene co-expression network analyses have become a central approach for the systems-level analysis of biological data.
Edit intent: clarity
Original: Background: Gene co-expression network analyses have become a central approach for the systems-level analysis of biological data.
Revised: Background: Gene co-expression network analyses have become a central approach for the systems-level study of biological data.
Edit intent: clarity
Original:  However, since some genes are able to up- or down-regulate other genes, it is important to explicitly consider both positive and negative correlations when constructing a gene co-expression network.
Revised:  However, since gene regulatory processes can up- or down-regulate other genes, it is important to explicitly consider both positive and negative correlations when constructing a gene co-expression network.
Edit intent: clarity
Original:  However, since some genes are able to up- or down-regulate other genes, it is important to explicitly consider both positive and negative correlations when constructing a gene co-expression network.
Revised:  However, since some genes are able to up- or down-regulate genes, it is important to explicitly consider both positive and negative correlations when constructing a gene co-expression network.
Edit intent: clarity
Original:  However, since some genes are able to up- or down-regulate other genes, it is important to explicitly consider both positive and negative correlations when constructing a gene co-expression network.
Revised:  However, since some genes are able to up- or down-regulate other genes, it is of great interest to explicitly consider both positive and negative correlations when constructing a gene co-expression network.
Edit intent: clarity
Original:  Results: Here, we present an R package for calculating the weighted topological overlap (wTO), that explicitly addresses the sign of wTO values .
Revised:  Results: Here, we present an R package for calculating the wTO, that, in contrast to existing packages, explicitly addresses the sign of wTO values .
Edit intent: clarity
Original:  Conclusion: In this work, we developed an R package that allows the computation of wTO networks, CNs and a visualization tool in the R statistical environment.
Revised:  Conclusion: In this work, we developed a software package that allows the computation of wTO networks, CNs and a visualization tool in the R statistical environment.
Edit intent: clarity
Original:  Two case studies, namely bacteria resource sharing and tumor cell signaling, are presented as examples to demonstrate the potential of this approach.
Revised:  Two case studies, namely bacteria resource sharing and tumor cell signaling, are presented with example games to demonstrate the potential of this approach.
Edit intent: clarity
Original: This article introduces the application of game theory to understand noisy real-time signaling and the resulting behavioral dynamics in microscopic populations such as bacteria and other cells.
Revised: This paper introduces the application of game theory to understand noisy real-time signaling and the resulting behavioral dynamics in microscopic populations such as bacteria and other cells.
Edit intent: fluency
Original: This article introduces the application of game theory to understand noisy real-time signaling and the resulting behavioral dynamics in microscopic populations such as bacteria and other cells.
Revised: This article introduces the application of game theory to understand noisy real-time signalling and the resulting behavioral dynamics in microscopic populations such as bacteria and other cells.
Edit intent: fluency
Original: This article introduces the application of game theory to understand noisy real-time signaling and the resulting behavioral dynamics in microscopic populations such as bacteria and other cells.
Revised: This article introduces the application of game theory to understand noisy real-time signaling and the resulting behavioural dynamics in microscopic populations such as bacteria and other cells.
Edit intent: fluency
Original:  Two case studies , namely bacteria quorum sensing and tumor cell signaling , are presented with example games to demonstrate the potential of this approach  .
Revised:  Two examples , namely bacteria quorum sensing and tumor cell signaling , are presented with example games to demonstrate the potential of this approach .
Edit intent: clarity
Original:  Two case studies , namely bacteria quorum sensing and tumor cell signaling , are presented with example games to demonstrate the potential of this approach  .
Revised:  Two case studies , namely bacteria quorum sensing and tumour cell signalling , are presented with example games to demonstrate the potential of this approach .
Edit intent: fluency
Original:  Two case studies , namely bacteria quorum sensing and tumor cell signaling , are presented with example games to demonstrate the potential of this approach  .
Revised:  Two case studies , namely bacteria quorum sensing and tumor cell signaling , are presented with potential games to demonstrate the potential of this approach .
Edit intent: clarity
Original:  Two case studies , namely bacteria quorum sensing and tumor cell signaling , are presented with example games to demonstrate the potential of this approach  .
Revised:  Two case studies , namely bacteria quorum sensing and tumor cell signaling , are presented with example games to demonstrate the application of this approach .
Edit intent: clarity
Original: We study a generalization of the Set Cover problem called the Partial Set Cover \emph{ in the context of geometric set systems.
Revised: We study a generalization of the Set Cover problem called the \emph{ in the context of geometric set systems.
Edit intent: clarity
Original: The distortion in steganography  comes from the modification or recoding on the cover image during the embedding process .
Revised: The distortion in steganography that usually comes from the modification or recoding on the cover image during the embedding process .
Edit intent: coherence
Original:  In GSK, we use a generator based on generative adversarial networks (GAN) to output the secret messages if and only if the data-hiding key and the cover image are both inputted.
Revised:  In GSK, we use a generator based on generative adversarial networks (GAN) to output the secret messages if and only if the extraction key and the cover image are both inputted.
Edit intent: clarity
Original:  In our training procedures, there are two GANs, Key-GAN and Cover-GAN, designed to work jointly making the generated results under the control of the data-hiding key and the cover image.
Revised:  In our training procedures, there are two GANs, Key-GAN and Cover-GAN, designed to work jointly making the generated results under the control of the extraction key and the cover image.
Edit intent: clarity
Original:  Experimental results concentrate on the training process and the working performance of GSK which demonstrate that GSK can use any image to realize steganography with Kerckhoffs' principle without any modification  .
Revised:  We provide experimental results on the training process and the working performance of GSK which demonstrate that GSK can use any image to realize steganography with Kerckhoffs' principle without any modification .
Edit intent: clarity
Original:  Experimental results concentrate on the training process and the working performance of GSK which demonstrate that GSK can use any image to realize steganography with Kerckhoffs' principle without any modification  .
Revised:  Experimental results concentrate on the training process and the working performance of GSK which demonstrate that GSK can use a cover image without any modification .
Edit intent: clarity
Original:  The resulting QT clustering (QTC) algorithm is shown to outperform the state-of-the-art spectral clustering method on synthetic and real data sets containing complex geometric patterns  .
Revised:  The resulting QT clustering (QTC) algorithm is as powerful as the state-of-the-art spectral clustering method on synthetic and real data sets containing complex geometric patterns .
Edit intent: clarity
Original:  The resulting QT clustering (QTC) algorithm is shown to outperform the state-of-the-art spectral clustering method on synthetic and real data sets containing complex geometric patterns  .
Revised:  The resulting QT clustering (QTC) algorithm is shown to outperform the state-of-the-art spectral clustering in discerning complex geometric patterns .
Edit intent: clarity
Original: We note that common implementations of  adaptive gradient algorithms, such as Adam , limit the potential benefit of weight decay regularization , because the weights do not decay multiplicatively (as would be expected for standard weight decay) but by an additive constant factor.
Revised: We note that common implementations ofnot adaptive gradient algorithms, such as Adam , limit the potential benefit of weight decay regularization , because the weights do not decay multiplicatively (as would be expected for standard weight decay) but by an additive constant factor.
Edit intent: fluency
Original:  While common deep learning frameworks of these algorithms implement L_2 regularization (often calling it "weight decay" in what may be misleading due to the inequivalence we expose), we propose a simple modification to recover the original formulation of weight decay regularization by decoupling the weight decay from the optimization steps taken w.r.t. the loss function.
Revised:  While common implementations of these algorithms implement L_2 regularization (often calling it "weight decay" in what may be misleading due to the inequivalence we expose), we propose a simple modification to recover the original formulation of weight decay regularization by decoupling the weight decay from the optimization steps taken w.r.t. the loss function.
Edit intent: clarity
Original:  While common deep learning frameworks of these algorithms implement L_2 regularization (often calling it "weight decay" in what may be misleading due to the inequivalence we expose), we propose a simple modification to recover the original formulation of weight decay regularization by decoupling the weight decay from the optimization steps taken w.r.t. the loss function.
Revised:  While common deep learning frameworks of these algorithms employ L_2 regularization (often calling it "weight decay" in what may be misleading due to the inequivalence we expose), we propose a simple modification to recover the original formulation of weight decay regularization by decoupling the weight decay from the optimization steps taken w.r.t. the loss function.
Edit intent: clarity
Original:  While common deep learning frameworks of these algorithms implement L_2 regularization (often calling it "weight decay" in what may be misleading due to the inequivalence we expose), we propose a simple modification to recover the original formulation of weight decay regularization by decoupling the weight decay from the optimization steps taken w.r.t. the loss function.
Revised:  While common deep learning frameworks of these algorithms implement L_2 regularization (often calling it "weight decay" in what may be misleading due to the inequivalence we expose), we propose a simple modification to recover the original formulation of weight decay regularization by decoupling the weight decay from the optimization steps taken w.r.t. the loss function.
Edit intent: fluency
Original:  We provide empirical evidence that our proposed modification (i) decouples the optimal choice of weight decay factor from the setting of the learning rate for both standard SGD and Adam , and (ii) substantially improves Adam's generalization performance, allowing it to compete with SGD with momentum on image classification datasets (on which it was previously typically outperformed by the latter).
Revised:  We provide empirical evidence that our proposed modification (i) decouples the optimal choice of weight decay factor from the setting of the learning rate for both standard SGD and Adam and (ii) substantially improves Adam's generalization performance, allowing it to compete with SGD with momentum on image classification datasets (on which it was previously typically outperformed by the latter).
Edit intent: fluency
Original: We describe categorical models of a circuit-based (quantum) functional pro- gramming language.
Revised: We describe categorical models of a circuit-based (quantum) functional programming language.
Edit intent: fluency
Original:  Tukey's bi-weight function is used as similarity function in the bilateral weighting, which is a robust estimator and stops the diffusion at sharp edges which helps to retain features and removes noise from flat regions effectively.
Revised:  Tukey's bi-weight function is used as similarity function in the bilateral weighting, which is a robust estimator and stops the diffusion at sharp edges which helps to retain features and removes noise from flat regions effectively.
Edit intent: fluency
Original:  Tukey's bi-weight function is used as similarity function in the bilateral weighting, which is a robust estimator and stops the diffusion at sharp edges which helps to retain features and removes noise from flat regions effectively.
Revised:  Tukey's bi-weight function is used as similarity function in the bilateral weighting, which is a robust estimator and stops the diffusion at sharp edges to retain features and removes noise from flat regions effectively.
Edit intent: coherence
Original:  In the second stage, an edge-weighted Laplace operator is introduced to compute the differential coordinate.
Revised:  In the second stage, an edge weighted Laplace operator is introduced to compute the differential coordinate.
Edit intent: fluency
Original:  In the second stage, an edge-weighted Laplace operator is introduced to compute the differential coordinate.
Revised:  In the second stage, an edge-weighted Laplace operator is introduced to compute a differential coordinate.
Edit intent: fluency
Original:  This differential coordinate helps the algorithm to produce a high-quality mesh without any face normal flips and also makes the method robust against high-intensity noise.
Revised:  This differential coordinate helps the algorithm to produce a high-quality mesh without any face normal flips and makes the method robust against high-intensity noise.
Edit intent: coherence
Original:  Each such equation can be stably discretized  .
Revised:  Each such equation can be stably discretized and solved .
Edit intent: clarity
Original: We investigate  computational complexity of questions of various problems for simple recurrent neural networks (RNNs) as formal models for recognizing weighted languages.
Revised: We investigate the computational complexity of questions of various problems for simple recurrent neural networks (RNNs) as formal models for recognizing weighted languages.
Edit intent: fluency
Original: We investigate  computational complexity of questions of various problems for simple recurrent neural networks (RNNs) as formal models for recognizing weighted languages.
Revised: We investigate computational complexity of various problems for simple recurrent neural networks (RNNs) as formal models for recognizing weighted languages.
Edit intent: clarity
Original:  We show that most problems for such RNNs are undecidable, including consistency, equivalence, minimization, and finding the highest-weighted string.
Revised:  We show that most problems for such RNNs are undecidable, including consistency, equivalence, minimization, and the determination of the highest-weighted string.
Edit intent: clarity
Original:  However, for consistent RNNs the last problem becomes decidable, although the solution can be exponentially long .
Revised:  However, for consistent RNNs the last problem becomes decidable, although the solution length can surpass all computable bounds .
Edit intent: clarity
Original:  In summary, this shows that approximations and heuristic algorithms are necessary in practical applications of those RNNs . We also consider RNNs as unweighted language recognizers and situate RNNs between Turing Machines and Random-Access Machines regarding their real-time recognition powers .
Revised:  In summary, this shows that approximations and heuristic algorithms are necessary in practical applications of those RNNs .
Edit intent: coherence
Original:  However, due to the sensitivity of information contained in such social graphs , they need to be properly anonymized before release.
Revised:  However, as social graphs contain sensitive information , they need to be properly anonymized before release.
Edit intent: clarity
Original:  Most of the graph anonymization techniques that have been proposed to sanitize social graph data rely on the perturbation of the original graph's structure, more specifically of its edge set.
Revised:  Most of the existing graph anonymization mechanisms rely on the perturbation of the original graph's structure, more specifically of its edge set.
Edit intent: clarity
Original:  Most of the graph anonymization techniques that have been proposed to sanitize social graph data rely on the perturbation of the original graph's structure, more specifically of its edge set.
Revised:  Most of the graph anonymization techniques that have been proposed to sanitize social graph data rely on the perturbation of the original graph's edge set.
Edit intent: clarity
Original:  First, we propose a method to quantify an edge's plausibility in a given graph by relying on graph embedding.
Revised:  First, we propose a method to quantify an edge's plausibility by relying on graph embedding.
Edit intent: clarity
Original:  Our experiments on three real-life social network datasets under two widely known graph anonymization mechanisms demonstrate that this method can very effectively detect fake edges with AUC values above 0.95 in most cases.
Revised:  Extensive experiments on three real-life social network datasets under two widely known graph anonymization mechanisms demonstrate that this method can very effectively detect fake edges with AUC values above 0.95 in most cases.
Edit intent: clarity
Original:  To mitigate this vulnerability, we propose a method to generate fake edges as plausible as possible given the graph structure and incorporate it into the existing anonymization mechanisms.
Revised:  To mitigate this vulnerability, we propose a method to generate fake yet plausible edges given the graph structure and incorporate it into the existing anonymization mechanisms.
Edit intent: clarity
Original:  Our evaluation demonstrates that the enhanced mechanisms not only decrease the chances of graph recovery (with AUC dropping by up to 35 \%), but also provide even better graph utility than existing anonymization methods .
Revised:  Our evaluation demonstrates that the enhanced mechanisms decrease the chances of graph recovery (with AUC dropping by up to 35 \%), but also provide even better graph utility than existing anonymization methods .
Edit intent: clarity