wanyu/IteraTeR_v2 huggingface dataset:
Original:  that is, for every graph F, the number of homomorphisms from F to G coincides with the number of homomorphisms from F to H.  }} Dell, Grohe, and Rattan showed that restrictions of the left-homomorphism vector to a class of graphs can capture several different relaxations of isomorphism, including  co-spectrality (i.e., two graphs having the same characteristic polynomial) , fractional isomorphism and, more broadly, equivalence in counting logics with a fixed number of variables .
Revised:  that is, for every graph F, the number of homomorphisms from F to G coincides with the number of homomorphisms from F to H. }} Dell, Grohe, and Rattan showed that restrictions of the left profile to a class of graphs can capture several different relaxations of isomorphism, including co-spectrality (i.e., two graphs having the same characteristic polynomial) , fractional isomorphism and, more broadly, equivalence in counting logics with a fixed number of variables .
Edit intent: clarity
Original:  In this paper, we embark on a study of the restrictions of the right-homomorphism vector by investigating relaxations of isomorphism that can or cannot be captured by restricting the right-homomorphism vector to a fixed class of graphs.
Revised:  In this paper, we embark on a study of the restrictions of the right-homomorphism vector by investigating relaxations of isomorphism that can or cannot be captured by restricting the right profile to a fixed class of graphs.
Edit intent: clarity
Original:  Our results unveil striking differences between the expressive power of the left-homomorphism vector and the right-homomorphism vector .
Revised:  Our results unveil striking differences between the expressive power of the left profile and the right profile .
Edit intent: style
Original:  We show that co-spectrality, fractional isomorphism, and equivalence in counting logics with a fixed number of variables  cannot be captured by restricting the right-homomorphism vector to a class of graphs.
Revised:  We show that fractional isomorphism, and equivalence in counting logics with a fixed number of variables cannot be captured by restricting the right-homomorphism vector to a class of graphs.
Edit intent: clarity
Original:  We show that co-spectrality, fractional isomorphism, and equivalence in counting logics with a fixed number of variables  cannot be captured by restricting the right-homomorphism vector to a class of graphs.
Revised:  We show that co-spectrality, fractional isomorphism, equivalence in counting logics with a fixed number of variables cannot be captured by restricting the right-homomorphism vector to a class of graphs.
Edit intent: fluency
Original:  We show that co-spectrality, fractional isomorphism, and equivalence in counting logics with a fixed number of variables  cannot be captured by restricting the right-homomorphism vector to a class of graphs.
Revised:  We show that co-spectrality, fractional isomorphism, and equivalence in counting logics with a fixed number of variables cannot be captured by restricting the right profile to a class of graphs.
Edit intent: clarity
Original:  In the opposite direction, we show that chromatic equivalence cannot be captured by restricting the left-homomorphism vector to a class of graphs, while, clearly, it can be captured by restricting the right-homomorphism vector to the class of all cliques.
Revised:  In the opposite direction, we show that chromatic equivalence cannot be captured by restricting the left profile to a class of graphs, while, clearly, it can be captured by restricting the right-homomorphism vector to the class of all cliques.
Edit intent: clarity
Original:  In the opposite direction, we show that chromatic equivalence cannot be captured by restricting the left-homomorphism vector to a class of graphs, while, clearly, it can be captured by restricting the right-homomorphism vector to the class of all cliques.
Revised:  In the opposite direction, we show that chromatic equivalence cannot be captured by restricting the left-homomorphism vector to a class of graphs, while, clearly, it can be captured by restricting the right profile to the class of all cliques.
Edit intent: clarity
Original:  WZs however also impose a space contraction resulting in adverse traffic operational and safety impacts, something that legitimately calls for benefiting from the highly efficient CAV mobility and safety functions.
Revised:  WZs however also impose a space contraction resulting in adverse traffic impacts, something that legitimately calls for benefiting from the highly efficient CAV mobility and safety functions.
Edit intent: clarity
Original:  WZs however also impose a space contraction resulting in adverse traffic operational and safety impacts, something that legitimately calls for benefiting from the highly efficient CAV mobility and safety functions.
Revised:  WZs however also impose a space contraction resulting in adverse traffic operational and safety impacts, something that legitimately calls for benefiting from the highly efficient CAV functions.
Edit intent: clarity
Original:   The paper also provides a review on the recent literature and summarizes a research agenda .
Revised:  In addition, among other topics reviewed and discussed are detection of WZ features, smart traffic control devices, various technologies at connected WZs, cross-border harmonization, liability, insurance, and privacy. The paper also provides a review on the recent literature and summarizes a research agenda .
Edit intent: coherence
Original:  The paper aims to provide a bird `s eye view, but with necessary details that can benefit practitioners, planners, and transportation agencies . Existing findings show that CAVs can credibly solve many WZ mobility and safety challenges, CAV benefits however are very sensitive to market penetration rate, traffic volume, communication technologies, and the assumed driver behaviour.
Revised:  The paper aims to provide a bird eye view, but with necessary details that can benefit practitioners, planners, and transportation agencies . Existing findings show that CAVs can credibly solve many WZ mobility and safety challenges, CAV benefits however are very sensitive to market penetration rate, traffic volume, communication technologies, and the assumed driver behaviour.
Edit intent: fluency
Original:  The paper aims to provide a bird `s eye view, but with necessary details that can benefit practitioners, planners, and transportation agencies . Existing findings show that CAVs can credibly solve many WZ mobility and safety challenges, CAV benefits however are very sensitive to market penetration rate, traffic volume, communication technologies, and the assumed driver behaviour.
Revised:  The paper aims to provide a bird `s eye view, but with necessary details that can benefit researchers, practitioners, and transportation agencies . Existing findings show that CAVs can credibly solve many WZ mobility and safety challenges, CAV benefits however are very sensitive to market penetration rate, traffic volume, communication technologies, and the assumed driver behaviour.
Edit intent: clarity
Original:  For the arbitrary high order DG method introduced in H. Liu and Z.
Revised:  H. Liu and Z.
Edit intent: coherence
Original:  In this paper we design a novel DG method, which with Euler forward time discretization is shown to preserve  positivity of cell averages at all time steps.
Revised:  In this paper we design a novel DG method, which with Euler forward time discretization is shown to preserve the positivity of cell averages at all time steps.
Edit intent: fluency
Original:  We consider the popular `tensor-train' (TT) format and ask , how efficiently can we compute a low-rank approximation from a full tensor on current multi-core CPUs . Compared to sparse and dense linear algebra, there are much fewer and less extensive well-optimized kernel libraries for multi-linear algebra  . Linear algebra libraries like BLAS and LAPACK may provide the required operations in principle, but often at the cost of additional data movements for rearranging memory layouts.
Revised:  We consider the popular `tensor-train' (TT) format and ask : How efficiently can we compute a low-rank approximation from a full tensor on current multi-core CPUs . Compared to sparse and dense linear algebra, there are much fewer and less extensive well-optimized kernel libraries for multi-linear algebra . Linear algebra libraries like BLAS and LAPACK may provide the required operations in principle, but often at the cost of additional data movements for rearranging memory layouts.
Edit intent: fluency
Original:  We consider the popular `tensor-train' (TT) format and ask , how efficiently can we compute a low-rank approximation from a full tensor on current multi-core CPUs . Compared to sparse and dense linear algebra, there are much fewer and less extensive well-optimized kernel libraries for multi-linear algebra  . Linear algebra libraries like BLAS and LAPACK may provide the required operations in principle, but often at the cost of additional data movements for rearranging memory layouts.
Revised:  We consider the popular `tensor-train' (TT) format and ask , how efficiently can we compute a low-rank approximation from a full tensor on current multi-core CPUs ? Compared to sparse and dense linear algebra, there are much fewer and less extensive well-optimized kernel libraries for multi-linear algebra . Linear algebra libraries like BLAS and LAPACK may provide the required operations in principle, but often at the cost of additional data movements for rearranging memory layouts.
Edit intent: fluency
Original:  We consider the popular `tensor-train' (TT) format and ask , how efficiently can we compute a low-rank approximation from a full tensor on current multi-core CPUs . Compared to sparse and dense linear algebra, there are much fewer and less extensive well-optimized kernel libraries for multi-linear algebra  . Linear algebra libraries like BLAS and LAPACK may provide the required operations in principle, but often at the cost of additional data movements for rearranging memory layouts.
Revised:  We consider the popular `tensor-train' (TT) format and ask , how efficiently can we compute a low-rank approximation from a full tensor on current multi-core CPUs . Compared to sparse and dense linear algebra, kernel libraries for multi-linear algebra . Linear algebra libraries like BLAS and LAPACK may provide the required operations in principle, but often at the cost of additional data movements for rearranging memory layouts.
Edit intent: coherence
Original:  In this work, we propose SCAN , aS patialC ontextA ttentiveN etwork that can jointly predict socially-acceptable multiple future trajectories for all pedestrians in a scene.
Revised:  In this work, we propose , aS patialC ontextA ttentiveN etwork that can jointly predict socially-acceptable multiple future trajectories for all pedestrians in a scene.
Edit intent: clarity
Original:  In this work, we propose SCAN , aS patialC ontextA ttentiveN etwork that can jointly predict socially-acceptable multiple future trajectories for all pedestrians in a scene.
Revised:  In this work, we propose SCAN S patialC ontextA ttentiveN etwork that can jointly predict socially-acceptable multiple future trajectories for all pedestrians in a scene.
Edit intent: fluency
Original:  In this work, we propose SCAN , aS patialC ontextA ttentiveN etwork that can jointly predict socially-acceptable multiple future trajectories for all pedestrians in a scene.
Revised:  In this work, we propose SCAN , a patialC ontextA ttentiveN etwork that can jointly predict socially-acceptable multiple future trajectories for all pedestrians in a scene.
Edit intent: fluency
Original:  In this work, we propose SCAN , aS patialC ontextA ttentiveN etwork that can jointly predict socially-acceptable multiple future trajectories for all pedestrians in a scene.
Revised:  In this work, we propose SCAN , aS C ontextA ttentiveN etwork that can jointly predict socially-acceptable multiple future trajectories for all pedestrians in a scene.
Edit intent: fluency
Original:  In this work, we propose SCAN , aS patialC ontextA ttentiveN etwork that can jointly predict socially-acceptable multiple future trajectories for all pedestrians in a scene.
Revised:  In this work, we propose SCAN , aS patial ontextA ttentiveN etwork that can jointly predict socially-acceptable multiple future trajectories for all pedestrians in a scene.
Edit intent: fluency
Original:  In this work, we propose SCAN , aS patialC ontextA ttentiveN etwork that can jointly predict socially-acceptable multiple future trajectories for all pedestrians in a scene.
Revised:  In this work, we propose SCAN , aS patialC A ttentiveN etwork that can jointly predict socially-acceptable multiple future trajectories for all pedestrians in a scene.
Edit intent: clarity
Original:  In this work, we propose SCAN , aS patialC ontextA ttentiveN etwork that can jointly predict socially-acceptable multiple future trajectories for all pedestrians in a scene.
Revised:  In this work, we propose SCAN , aS patialC ontext ttentiveN etwork that can jointly predict socially-acceptable multiple future trajectories for all pedestrians in a scene.
Edit intent: fluency
Original:  In this work, we propose SCAN , aS patialC ontextA ttentiveN etwork that can jointly predict socially-acceptable multiple future trajectories for all pedestrians in a scene.
Revised:  In this work, we propose SCAN , aS patialC ontextA N etwork that can jointly predict socially-acceptable multiple future trajectories for all pedestrians in a scene.
Edit intent: fluency
Original:  In this work, we propose SCAN , aS patialC ontextA ttentiveN etwork that can jointly predict socially-acceptable multiple future trajectories for all pedestrians in a scene.
Revised:  In this work, we propose SCAN , aS patialC ontextA ttentive etwork that can jointly predict socially-acceptable multiple future trajectories for all pedestrians in a scene.
Edit intent: fluency
Original:  Not only to the music industry, the biomedical , and healthcare industry can also exploit this experiment to collect data from patients to improve the efficiency of healing by music.
Revised:  Not only to the music industry, the biomedical and healthcare industry can also exploit this experiment to collect data from patients to improve the efficiency of healing by music.
Edit intent: fluency
Original:  The results generate SteemOps, a new dataset that organizes over 900 million operations from Steemit into three sub-datasets : 1 ) social-network operation dataset (SOD) ;
Revised:  The results generate SteemOps, a new dataset that organizes more than 900 million operations from Steemit into three sub-datasets : 1 ) social-network operation dataset (SOD) ;
Edit intent: fluency
Original:  We describe the dataset schema and its usage in detail and outline various potential research directions based on SteemOps.
Revised:  We describe the dataset schema and its usage in detail and outline possible future research studies using SteemOps.
Edit intent: clarity
Original:  SteemOps is designed to facilitate future studies aimed at providing better insights on emerging blockchain-based social media platforms.
Revised:  SteemOps is designed to facilitate future research aimed at providing better insights on emerging blockchain-based social media platforms.
Edit intent: clarity
Original:  State-of-the-art speech representation learning methods for more speech factors are using primary disentangle algorithms such as random resampling and ad-hoc bottleneck layer size adjustment,which however is hard to ensure robust speech representation disentanglement .
Revised:  State-of-the-art speech representation learning methods for more speechfactors are using primary disentangle algorithms such as random resampling and ad-hoc bottleneck layer size adjustment,which however is hard to ensure robust speech representation disentanglement .
Edit intent: fluency
Original:  State-of-the-art speech representation learning methods for more speech factors are using primary disentangle algorithms such as random resampling and ad-hoc bottleneck layer size adjustment,which however is hard to ensure robust speech representation disentanglement .
Revised:  State-of-the-art speech representation learning methods for more speech factors are using primary disentangle algorithms such as random resampling and ad-hoc bottleneck layer size adjustment,which however is hard to ensure robust speech representationdisentanglement .
Edit intent: fluency
Original:  The adversarial network is used to minimize the correlations between the speech representations,by randomly masking and predicting one of the representations from the others.
Revised:  The adversarial network is used tominimize the correlations between the speech representations,by randomly masking and predicting one of the representations from the others.
Edit intent: fluency
Original:  The adversarial network is used to minimize the correlations between the speech representations,by randomly masking and predicting one of the representations from the others.
Revised:  The adversarial network is used to minimize the correlations between the speech representations,by randomly masking and predicting one of the representationsfrom the others.
Edit intent: fluency
Original:  A word prediction network is also adopted to learn a more informative content representation.
Edit intent: coherence
Original:  Experimental results show that the proposed speech representation learning framework significantly improves the robustness of VC on multiple factors by increasing conversion rate from 48.2\% to 57.1\% and ABX preference exceeding by 31.2\% compared with state-of-the-art method .
Revised:  Experimental results show that the proposedframework significantly improves the robustness of VC on multiple factors by increasing conversion rate from 48.2\% to 57.1\% and ABX preference exceeding by 31.2\% compared with state-of-the-art method .
Edit intent: clarity
Original: The origin(s) of the ubiquity of Zipf's law (an inverse power law form for the probability density function (PDF) with exponent 1+1) is still a matter of fascination and investigation in many scientific fields from linguistic, social, economic, computer sciences to essentially all natural sciences.
Revised: The origin(s) of the ubiquity of probability distribution functions (PDF) with exponent 1+1) is still a matter of fascination and investigation in many scientific fields from linguistic, social, economic, computer sciences to essentially all natural sciences.
Edit intent: clarity
Original: The origin(s) of the ubiquity of Zipf's law (an inverse power law form for the probability density function (PDF) with exponent 1+1) is still a matter of fascination and investigation in many scientific fields from linguistic, social, economic, computer sciences to essentially all natural sciences.
Revised: The origin(s) of the ubiquity of Zipf's law (an inverse power law form for the probability density function (PDF) with power law tails is still a matter of fascination and investigation in many scientific fields from linguistic, social, economic, computer sciences to essentially all natural sciences.
Edit intent: clarity
Original:  Solving the corresponding master equations, we find that a wide class of such nonlinear Hawkes processes have the PDF of their intensities described by Zipf's law on the condition that (i) the intensity is a fast-accelerating function of tension and (ii) the distribution of the point fertilities is symmetric .
Revised:  Solving the corresponding master equations, we find that a wide class of such nonlinear Hawkes processes have the PDF of their intensities described by Zipf's law on the condition that (i) the intensity is a fast-accelerating function of tension , (ii) the distribution of the point fertilities is symmetric .
Edit intent: fluency
Original:  This unearths a novel mechanism for  Zipf's law, providing a new understanding of its ubiquity.
Revised:  This unearths a novel mechanism for Zipf's law, providing a new understanding of their ubiquity.
Edit intent: fluency
Original: This paper presents a wearable electrotactile feedback system to enable precise and accurate contact rendering with virtual objects for mid-air interactions  .
Revised: This paper presents a wearable electrotactile feedback system to enhance contact information for mid-air interactions .
Edit intent: clarity
Original: This paper presents a wearable electrotactile feedback system to enable precise and accurate contact rendering with virtual objects for mid-air interactions  .
Revised: This paper presents a wearable electrotactile feedback system to enable precise and accurate contact rendering with virtual objects for mid-air interactions with virtual objects .
Edit intent: fluency
Original:  Taken together, these results suggest that electrotactile feedback could be an efficient replacement of visual feedback for accurate and precise contact rendering in virtual reality avoiding the need of active visual focus and the rendering of additional visual artefacts.
Revised:  Taken together, these results suggest that electrotactile feedback could be an efficient replacement of visual feedback for enhancing contact information in virtual reality avoiding the need of active visual focus and the rendering of additional visual artefacts.
Edit intent: clarity
Original: We demonstrate that matching the symmetry properties of a reservoir computer (RC) to the data being processed can dramatically increase its processing power.
Revised: We match the symmetry properties of a reservoir computer (RC) to the data being processed can dramatically increase its processing power.
Edit intent: clarity
Original: We demonstrate that matching the symmetry properties of a reservoir computer (RC) to the data being processed can dramatically increase its processing power.
Revised: We demonstrate that matching the symmetry properties of a reservoir computer (RC) to the data being processed dramatically increasing its processing power.
Edit intent: clarity
Original:  The symmetry-aware RC can obtain zero error using an exponentially reduced number of artificial neurons and training data, greatly speeding up the time-to-result  .
Revised:  The symmetry-aware RC obtains zero error using an exponentially reduced number of artificial neurons and training data, greatly speeding up the time-to-result .
Edit intent: clarity
Original:  The symmetry-aware RC can obtain zero error using an exponentially reduced number of artificial neurons and training data, greatly speeding up the time-to-result  .
Revised:  The symmetry-aware RC can obtain zero error using an exponentially reduced artificial neurons and training data, greatly speeding up the time-to-result .
Edit intent: clarity
Original: We match the symmetry properties of a reservoir computer (RC) to the data being processed dramatically increasing its processing power.
Revised: We demonstrate that matching the symmetry properties of a reservoir computer (RC) to the data being processed dramatically increasing its processing power.
Edit intent: clarity
Original: We match the symmetry properties of a reservoir computer (RC) to the data being processed dramatically increasing its processing power.
Revised: We match the symmetry properties of a reservoir computer (RC) to the data being processed dramatically increases its processing power.
Edit intent: fluency
Original:  For the parity task, our symmetry-aware RC obtains zero error using an exponentially reduced artificial neurons and training data, greatly speeding up the time-to-result and outperforming hand crafted artificial neural networks (ANN)\leq7 . For the inference task, the performance is orders-of-magnitude better than regular RCs.
Revised:  For the parity task, our symmetry-aware RC obtains zero error using an exponentially reduced neural network and training data, greatly speeding up the time-to-result and outperforming hand crafted artificial neural networks (ANN)\leq7 . For the inference task, the performance is orders-of-magnitude better than regular RCs.
Edit intent: clarity