wanyu/IteraTeR_v2 huggingface dataset:
Original: In this paper, we develop a new notion of entropy for uniform hypergraphs , which are generalized from graphs , based on tensor theory.
Revised: In this paper, we develop a new notion of entropy for uniform hypergraphs , which are generalized from graphs based on tensor theory.
Edit intent: fluency
Original:  In particular, we employ the probability distribution of the generalized singular values, calculated from the higher-order singular value decomposition of the Laplacian tensors, to fit into the Shannon entropy formula.
Revised:  We employ the probability distribution of the generalized singular values, calculated from the higher-order singular value decomposition of the Laplacian tensors, to fit into the Shannon entropy formula.
Edit intent: coherence
Original:  It is shown that this tensor entropy is an extension of von Neumann entropy for graphs.
Revised:  We show that this tensor entropy is an extension of von Neumann entropy for graphs.
Edit intent: coherence
Original:  We establish results on the lower and upper bounds of the entropy and demonstrate that it is a measure of regularity , relying on the vertex degrees, path lengths, clustering coefficients and nontrivial symmetricity, for uniform hypergraphs with two simulated examples .
Revised:  In addition, we establish results on the lower and upper bounds of the entropy and demonstrate that it is a measure of regularity , relying on the vertex degrees, path lengths, clustering coefficients and nontrivial symmetricity, for uniform hypergraphs with two simulated examples .
Edit intent: coherence
Original:  We establish results on the lower and upper bounds of the entropy and demonstrate that it is a measure of regularity , relying on the vertex degrees, path lengths, clustering coefficients and nontrivial symmetricity, for uniform hypergraphs with two simulated examples .
Revised:  We establish results on the lower and upper bounds of the entropy and demonstrate that it is a measure of regularity for uniform hypergraphs with two simulated examples .
Edit intent: coherence
Original:  Finally, we exploit the tensor train decomposition in computing the proposed tensor entropy efficiently  .
Revised:  We exploit the tensor train decomposition in computing the proposed tensor entropy efficiently .
Edit intent: coherence
Original: In this paper, we study the error behavior of the known  fast Fourier transform for nonequispaced data (NFFT).
Revised: In this paper, we study the error behavior of the known fast Fourier transform (NFFT).
Edit intent: clarity
Original:  We present novel uniform error estimates for NFFT  and derive rules for the optimal choice from the parameters involved in NFFT  .
Revised:  We present novel error estimates for NFFT and derive rules for the optimal choice from the parameters involved in NFFT .
Edit intent: clarity
Original: In this paper, we study the error behavior of the known nonequispaced fast Fourier transform (NFFT).
Revised: In this paper, we study the error behavior of the nonequispaced fast Fourier transform (NFFT).
Edit intent: clarity
Original:  We present novel error estimates for NFFT with compactly supported, continuous window function and derive rules for the optimal choice from the parameters involved in NFFT.
Revised:  We present novel error estimates for NFFT with compactly supported, continuous window functions and derive rules for the optimal choice from the parameters involved in NFFT.
Edit intent: fluency
Original:  We present novel error estimates for NFFT with compactly supported, continuous window functions and derive rules for the optimal choice from the parameters involved in NFFT.
Revised:  We present novel error estimates for NFFT with compactly supported, continuous window functions and derive rules for convenient choice from the parameters involved in NFFT.
Edit intent: clarity
Original: Availability codes have recently been proposed to facilitate efficient storage, management, and retrieval of frequently accessed data in distributed storage systems.
Revised: Availability codes have recently been proposed to facilitate efficient retrieval of frequently accessed data in distributed storage systems.
Edit intent: clarity
Original: Availability codes have recently been proposed to facilitate efficient storage, management, and retrieval of frequently accessed data in distributed storage systems.
Revised: Availability codes have recently been proposed to facilitate efficient storage, management, and retrieval of frequently accessed (hot) data objects in distributed storage systems.
Edit intent: clarity
Original:  We first carry out the analysis under the low-traffic regime in which case the system consists of at most one download request at any time.
Revised:  We first carry out the analysis under the low-traffic regime , when there is at most one download request at any time.
Edit intent: clarity
Original:  Our results indicate that availability codes can reduce download time in some settings, but are not always optimal.
Revised:  We demonstrate that availability codes can reduce download time in some settings, but are not always optimal.
Edit intent: clarity
Original:  When the low-traffic assumption does not hold, system consists of multiple inter-dependent Fork-Join queues operating in parallel , which makes the exact analysis intractable  .
Revised:  When the low-traffic assumption does not hold, system consists of multiple inter-dependent Fork-Join queues , which makes the exact analysis intractable .
Edit intent: clarity
Original:  When the low-traffic assumption does not hold, system consists of multiple inter-dependent Fork-Join queues operating in parallel , which makes the exact analysis intractable  .
Revised:  When the low-traffic assumption does not hold, system consists of multiple inter-dependent Fork-Join queues operating in parallel , which makes exact analysis intractable .
Edit intent: fluency
Original:  For this case  we present upper and lower bounds on the download time .
Revised:  For this case , we present upper and lower bounds on the download time .
Edit intent: fluency
Original:  Such codes provide multiple disjoint recovery groups for each data object, thus providing flexibility in accessing data objects.
Edit intent: coherence
Original:  With the Fork-Join access scheme, each data request is replicated (forked) to the systematic server containing the object and all of its recovery groups.
Revised:  Specifically, we consider the setup in which requests arrive for downloading individual data objects, and each request is replicated (forked) to the systematic server containing the object and all of its recovery groups.
Edit intent: clarity
Original:  For this case , we present upper and lower bounds on the download time, and an M/G/1 queue approximation for several special cases of interest.
Revised:  Here , we present upper and lower bounds on the download time, and an M/G/1 queue approximation for several special cases of interest.
Edit intent: coherence
Original:  Via  numerical simulations, we evaluate our bounds, and demonstrate that the M/G/1 queue approximation has a high degree of accuracy .
Revised:  Via extensive numerical simulations, we evaluate our bounds, and demonstrate that the M/G/1 queue approximation has a high degree of accuracy .
Edit intent: clarity
Original:  This paper presents techniques for analyzing the download time of systematic availability codes considering the Fork-Join scheme for data access.
Revised:  This paper presents techniques for analyzing the expected download time in distributed storage systems that employ systematic availability codes considering the Fork-Join scheme for data access.
Edit intent: clarity
Original:  Specifically, we consider the setup in which requests arrive for downloading individual data objects, and each request is replicated (forked) to the systematic server containing the object and all of its recovery groups.
Revised:  Specifically, we consider the setup in which requests arrive for downloading individual data objects, and each request is replicated (forked) to the systematic server and all recovery groups.
Edit intent: clarity
Original:  We demonstrate that availability codes can reduce download time in some settings , but are not always optimal.
Revised:  We demonstrate that availability codes can reduce download time in some settings but are not always optimal.
Edit intent: fluency
Original:  When the low-traffic assumption does not hold, system consists of multiple inter-dependent Fork-Join queues, which makes exact analysis intractable due to state space explosion.
Revised:  In the high-traffic regime, the system consists of multiple inter-dependent Fork-Join queues, which makes exact analysis intractable due to state space explosion.
Edit intent: clarity
Original:  When the low-traffic assumption does not hold, system consists of multiple inter-dependent Fork-Join queues, which makes exact analysis intractable due to state space explosion.
Revised:  When the low-traffic assumption does not hold, system consists of multiple inter-dependent Fork-Join queues, making exact analysis intractable due to state space explosion.
Edit intent: coherence
Original:  Here , we present upper and lower bounds on the download time, and an M/G/1 queue approximation for several special cases of interest.
Revised:  Here , we present upper and lower bounds on the download time, and an M/G/1 queue approximation for several cases of interest.
Edit intent: clarity
Original:  Via extensive numerical simulations, we evaluate our bounds , and demonstrate that the M/G/1 queue approximation has a high degree of accuracy.
Revised:  Via extensive numerical simulations, we evaluate our bounds and demonstrate that the M/G/1 queue approximation has a high degree of accuracy.
Edit intent: fluency
Original:  It is known that the attributes may clarify and enrich the knowledge about the actors and give sense to the detected communities.
Revised:  It is known that the attributes may clarify and enrich the knowledge about the actors and give sense to the communities.
Edit intent: clarity
Original:  During the last decade many  methods based on different ideas and techniques have appearedin this direction .
Revised:  During the last decade many such methods based on different ideas and techniques have appearedin this direction .
Edit intent: clarity
Original:  During the last decade many  methods based on different ideas and techniques have appearedin this direction .
Revised:  During the last decade many methods based on different ideas have appeared .
Edit intent: clarity
Original:  Although there exist some partial overviews of them, a recent survey is a necessity as the growing number of the methods may cause  uncertainty in practice.
Revised:  Although there exist partial overviews of them, a recent survey is a necessity as the growing number of the methods may cause uncertainty in practice.
Edit intent: fluency
Original:  In this paper we aim at  clarifying the overall situation by proposing a clear classification of the methods and providing a comprehensive survey of the available results .
Revised:  In this paper we aim at describing and clarifying the overall situation by proposing a clear classification of the methods and providing a comprehensive survey of the available results .
Edit intent: clarity
Original: The growing momentum of instrumenting the Internet of Things (IoT) with advanced machine learning techniques such as deep neural networks (DNNs) faces two practical challenges of limited compute power of edge devices and the need of protecting the confidentiality of the DNNs.
Revised: Executing deep neural networks (DNNs) faces two practical challenges of limited compute power of edge devices and the need of protecting the confidentiality of the DNNs.
Edit intent: clarity
Original: The growing momentum of instrumenting the Internet of Things (IoT) with advanced machine learning techniques such as deep neural networks (DNNs) faces two practical challenges of limited compute power of edge devices and the need of protecting the confidentiality of the DNNs.
Revised: The growing momentum of instrumenting the Internet of Things (IoT) with advanced machine learning techniques such as deep neural networks (DNNs) faces two practical challenges of limited compute power of edge devices and the need to protect the confidentiality of the DNNs.
Edit intent: fluency
Original:  The evaluation results obtained from the case studies show that our approach prevents the backend from obtaining the raw forms of the inference data while maintaining the DNN 's inference accuracy at the backend .
Revised:  The evaluation results obtained from the case studies show that our approach effectively protects the confidentiality of the raw forms of the inference data while maintaining the DNN 's inference accuracy at the backend .
Edit intent: clarity
Original:  The evaluation results obtained from the case studies show that our approach prevents the backend from obtaining the raw forms of the inference data while maintaining the DNN 's inference accuracy at the backend .
Revised:  The evaluation results obtained from the case studies show that our approach prevents the backend from obtaining the raw forms of the inference data while effectively preserving the backend 's inference accuracy at the backend .
Edit intent: clarity
Original:  The evaluation results obtained from the case studies show that our approach prevents the backend from obtaining the raw forms of the inference data while maintaining the DNN 's inference accuracy at the backend .
Revised:  The evaluation results obtained from the case studies show that our approach prevents the backend from obtaining the raw forms of the inference data while maintaining the DNN 's inference accuracy .
Edit intent: clarity
Original: In this paper we present an efficient and fully error controlled algorithm for yield estimation and yield optimization .
Revised: In this paper we present an algorithm for yield estimation and yield optimization .
Edit intent: clarity
Original:  Since computational efficiency is one main issue in uncertainty quantification, we propose a hybrid method, where a large part of a Monte Carlo (MC ) sample is evaluated with a surrogate model, and only a small subset of the sample is re-evaluated with a high fidelity finite element model.
Revised:  Since computational efficiency is one main issue in uncertainty quantification, we propose a hybrid method, where a large part of a MC sample is evaluated with a surrogate model, and only a small subset of the sample is re-evaluated with a high fidelity finite element model.
Edit intent: clarity
Original:  We reduce computational effort and control the MC error by adaptivly increasing the sample size.
Revised:  We reduce computational effort and control the MC error by adaptively increasing the sample size.
Edit intent: fluency
Original:  There seems to be one constant: the only useful example of an algebra of probabilities is the real unit interval (or a subalgebra of some product of them) .
Revised:  There seems to be one constant: the only useful example of an algebra of probabilities is the real unit interval .
Edit intent: clarity
Original:  Intuitively then, each such effect monoid splits up into a 'sharp ' part represented by the Boolean algebra , and a 'probabilistic ' part represented by the commutative C^*-algebra.
Revised:  This gives us from first principles a dichotomy between sharp logic, represented by the Boolean algebra , and a 'probabilistic ' part represented by the commutative C^*-algebra.
Edit intent: clarity
Original:  Some consequences of this characterization are that the multiplication must always be commutative, and that the unique \omega-complete effect monoid without zero divisors and more than 2 elements must be the real unit interval.
Revised:  Some consequences of this characterisation are that the multiplication must always be commutative, and that the unique \omega-complete effect monoid without zero divisors and more than 2 elements must be the real unit interval.
Edit intent: clarity
Original:  Our results give an algebraic characterization and motivation for why any physical or logical theory would represent probabilities by real numbers.
Revised:  Our results give an algebraic characterisation and motivation for why any physical or logical theory would represent probabilities by real numbers.
Edit intent: fluency
Original:  Compared to %DIFDELCMD < {\sf %%% Myerson Auction , whose sample complexity was settled very recently in (Guo, Huang and Zhang, STOC ~ 2019), %DIFDELCMD < {\sf %%% Anonymous Reserve requires much fewer samples for learning.
Revised:  Compared to %DIFDELCMD < {\sf %%% Myerson Auction , whose sample complexity was settled very recently in (Guo, Huang and Zhang, STOC ~ 2019), %DIFDELCMD < {\sf %%% Anonymous Reserve requires much fewer samples for learning.
Edit intent: fluency
Original:  Compared to %DIFDELCMD < {\sf %%% Myerson Auction , whose sample complexity was settled very recently in (Guo, Huang and Zhang, STOC ~ 2019), %DIFDELCMD < {\sf %%% Anonymous Reserve requires much fewer samples for learning.
Revised:  Compared to %DIFDELCMD < {\sf %%% Myerson Auction , whose sample complexity was settled very recently in (Guo, Huang and Zhang, STOC 2019), %DIFDELCMD < {\sf %%% Anonymous Reserve requires much fewer samples for learning.
Edit intent: fluency
Original: The minimal path model based on the Eikonal partial differential equation (PDE) has served as a fundamental tool for the applications of image segmentation and boundary detection in the passed three decades.
Revised: The minimal path model based on the Eikonal partial differential equation has served as a fundamental tool for the applications of image segmentation and boundary detection in the passed three decades.
Edit intent: clarity
Original:  However, the existing minimal paths-based image segmentation approaches commonly rely on the image boundary features , potentially limiting their performance in some situations.
Revised:  However, the existing approaches commonly only exploit the image edge-based features for computing minimal paths , potentially limiting their performance in some situations.
Edit intent: clarity
Original:  However, the existing minimal paths-based image segmentation approaches commonly rely on the image boundary features , potentially limiting their performance in some situations.
Revised:  However, the existing minimal paths-based image segmentation approaches commonly rely on the image boundary features , potentially limiting their performance in complicated segmentation situations.
Edit intent: clarity
Original:  In this paper, we introduce a new variational image segmentation model based on the minimal path framework and the Eikonal PDE, where the region-based functional that defines the homogeneity criteria can be taken into account for estimating the associated geodesic paths.
Revised:  In this paper, we introduce a new variational image segmentation model based on the minimal path framework and the eikonal PDE, where the region-based functional that defines the homogeneity criteria can be taken into account for estimating the associated geodesic paths.
Edit intent: fluency
Original:  In this paper, we introduce a new variational image segmentation model based on the minimal path framework and the Eikonal PDE, where the region-based functional that defines the homogeneity criteria can be taken into account for estimating the associated geodesic paths.
Revised:  In this paper, we introduce a new variational image segmentation model based on the minimal path framework and the Eikonal PDE, where the region-based appearance term that defines then regional homogeneity features can be taken into account for estimating the associated geodesic paths.
Edit intent: clarity
Original:  In this paper, we introduce a new variational image segmentation model based on the minimal path framework and the Eikonal PDE, where the region-based functional that defines the homogeneity criteria can be taken into account for estimating the associated geodesic paths.
Revised:  In this paper, we introduce a new variational image segmentation model based on the minimal path framework and the Eikonal PDE, where the region-based functional that defines the homogeneity criteria can be taken into account for estimating the associated minimal paths.
Edit intent: clarity
Original:  The object boundary can be delineated by the concatenation of the final geodesic paths.
Revised:  The object boundary can be delineated by the concatenation of the piecewise geodesic paths.
Edit intent: clarity
Original:  Experimental results on both of the synthetic and real images exhibit that our model indeed achieves encouraging segmentation performance.
Revised:  Experimental results on both synthetic and real images exhibit that our model indeed achieves encouraging segmentation performance.
Edit intent: clarity
Original:  Image classifiers trained with JARN show improved robust accuracy compared to standard models on the MNIST, SVHN and CIFAR-10 datasets, uncovering a new angle to boost robustness without using adversarial training  .
Revised:  Image classifiers trained with JARN show improved robust accuracy compared to standard models on the MNIST, SVHN and CIFAR-10 datasets, uncovering a new angle to boost robustness without using adversarial training examples .
Edit intent: clarity
Original:  Both one and two dimensional numerical examples verify our theoretical results, and demonstrate the good performance of EQ-DG on efficiency, accuracy, and preservation of the desired solution properties.
Revised:  Both one and two dimensional numerical examples are provided to verify the theoretical results, and demonstrate the good performance of EQ-DG on efficiency, accuracy, and preservation of the desired solution properties.
Edit intent: clarity
Original:  Both one and two dimensional numerical examples verify our theoretical results, and demonstrate the good performance of EQ-DG on efficiency, accuracy, and preservation of the desired solution properties.
Revised:  Both one and two dimensional numerical examples verify our theoretical results, and demonstrate the good performance of IEQ-DG in terms of efficiency, accuracy, and preservation of the desired solution properties.
Edit intent: clarity
Original: Many organizations recognize non-terrestrial communication (NTC ) as a key component to provide cost-effective and high-capacity connectivity in future 6th generation (6G) wireless networks.
Revised: Many organizations recognize non-terrestrial networks (NTNs ) as a key component to provide cost-effective and high-capacity connectivity in future 6th generation (6G) wireless networks.
Edit intent: clarity
Original:  In this paper, we review the characteristics and enabling technologies of non-terrestrial systems in the 6G landscape and shed light on the challenges in the field that are still open for future research.
Revised:  In this paper, we review the characteristics and enabling technologies of NTNs in the 6G landscape and shed light on the challenges in the field that are still open for future research.
Edit intent: clarity
Original:  As a case study, we also evaluate the performance of an NTC scenario in which satellites use millimeter wave (mmWave) frequencies to provide access connectivity to on-the-ground mobile terminals as a function of different networking configurations.
Revised:  As a case study, we evaluate the performance of an NTC scenario in which satellites use millimeter wave (mmWave) frequencies to provide access connectivity to on-the-ground mobile terminals as a function of different networking configurations.
Edit intent: clarity
Original:  As a case study, we also evaluate the performance of an NTC scenario in which satellites use millimeter wave (mmWave) frequencies to provide access connectivity to on-the-ground mobile terminals as a function of different networking configurations.
Revised:  As a case study, we also evaluate the performance of an NTN scenario in which satellites use millimeter wave (mmWave) frequencies to provide access connectivity to on-the-ground mobile terminals as a function of different networking configurations.
Edit intent: clarity