wanyu/IteraTeR_v2 huggingface dataset:
Original:  A novel quirk of this approach is that the usual empty definitions with \epsilon parts are eschewed in favour of optional parts in the right recursive rules that the algorithm generates .
Revised:  Furthermore, the vacuous definitions with \epsilon parts are eschewed in favour of optional parts in the right recursive rules that the algorithm generates .
Edit intent: clarity
Original: We present the construction of Hybrid Monte Carlo (HMC) algorithms for constrained Hamiltonian systems of gauge-Higgs models in order to measure the constraint effective Higgs potential.
Revised: We develop Hybrid Monte Carlo (HMC) algorithms for constrained Hamiltonian systems of gauge-Higgs models in order to measure the constraint effective Higgs potential.
Edit intent: clarity
Original:  We develop new methods to measure constraint effective potentials, using an extension of the so-called Rattle algorithm to general Hamiltonians for constrained systems, which we adapt to the 4D Abelian gauge-Higgs model and the 5D SU(2) gauge theory on the torus and on the orbifold.
Revised:  We develop new methods to measure constraint effective potentials, using an extension of the so-called Rattle algorithm to general Hamiltonians for constrained systems, which we adapt to the 4D Abelian-Higgs model and the 5D SU(2) gauge theory on the torus and on the orbifold.
Edit intent: fluency
Original:  The derivative of the potential is determined via the expectation value of the Lagrange multiplier for the constraint  .
Revised:  The derivative of the potential is measured via the expectation value of the Lagrange multiplier for the constraint .
Edit intent: clarity
Original: Music has been one of the strongest forms of cultural expression and identity for thousands of years and has evolved into a strongly collaborative artistic domain.
Edit intent: coherence
Original:  While the emergence of success in music has been studied at large , the link between individual success and collaboration has not yet been fully uncovered.
Revised:  While the emergence of success in creative professions, such as music, has been studied at large , the link between individual success and collaboration has not yet been fully uncovered.
Edit intent: clarity
Original:  While the emergence of success in music has been studied at large , the link between individual success and collaboration has not yet been fully uncovered.
Revised:  While the emergence of success in music has been studied extensively , the link between individual success and collaboration has not yet been fully uncovered.
Edit intent: clarity
Original:  While the emergence of success in music has been studied at large , the link between individual success and collaboration has not yet been fully uncovered.
Revised:  While the emergence of success in music has been studied at large , the link between individual success and collaboration is not yet fully uncovered.
Edit intent: fluency
Original:  Here we aim to fill this gap by analyzing longitudinal data on the co-releasing and mentoring patterns of tens of thousands of electronic music artists , the most popular of them appearing in the annual Top 100 ranking of the DJ Magazine.
Revised:  Here we aim to fill this gap by analyzing longitudinal data on the co-releasing and mentoring patterns of popular electronic music artists , the most popular of them appearing in the annual Top 100 ranking of the DJ Magazine.
Edit intent: clarity
Original:  Here we aim to fill this gap by analyzing longitudinal data on the co-releasing and mentoring patterns of tens of thousands of electronic music artists , the most popular of them appearing in the annual Top 100 ranking of the DJ Magazine.
Revised:  Here we aim to fill this gap by analyzing longitudinal data on the co-releasing and mentoring patterns of tens of thousands of electronic music artists appearing in the annual Top 100 ranking of the DJ Magazine.
Edit intent: clarity
Original:  Here we aim to fill this gap by analyzing longitudinal data on the co-releasing and mentoring patterns of tens of thousands of electronic music artists , the most popular of them appearing in the annual Top 100 ranking of the DJ Magazine.
Revised:  Here we aim to fill this gap by analyzing longitudinal data on the co-releasing and mentoring patterns of tens of thousands of electronic music artists , the most popular of them appearing in the annual Top 100 ranking of DJ Magazine.
Edit intent: fluency
Original:  We find that while this ranking list of popularity publishes the Top 100 names, only the top 20 is relatively stable in time, showcasing a lock-in effect on the stars of electronic music . Based on the temporal co-release network of Top 100 musicians, we uncover a diverse community structure characterizing the electronic music industry.
Revised:  We find that while this ranking list of popularity publishes 100 names, only the top 20 is relatively stable in time, showcasing a lock-in effect on the stars of electronic music . Based on the temporal co-release network of Top 100 musicians, we uncover a diverse community structure characterizing the electronic music industry.
Edit intent: fluency
Original:  We find that while this ranking list of popularity publishes the Top 100 names, only the top 20 is relatively stable in time, showcasing a lock-in effect on the stars of electronic music . Based on the temporal co-release network of Top 100 musicians, we uncover a diverse community structure characterizing the electronic music industry.
Revised:  We find that while this ranking list of popularity publishes the Top 100 names, only the top 20 is stable over time, showcasing a lock-in effect on the stars of electronic music . Based on the temporal co-release network of Top 100 musicians, we uncover a diverse community structure characterizing the electronic music industry.
Edit intent: clarity
Original:  We find that while this ranking list of popularity publishes the Top 100 names, only the top 20 is relatively stable in time, showcasing a lock-in effect on the stars of electronic music . Based on the temporal co-release network of Top 100 musicians, we uncover a diverse community structure characterizing the electronic music industry.
Revised:  We find that while this ranking list of popularity publishes the Top 100 names, only the top 20 is relatively stable in time, showcasing a lock-in effect on the electronic music elite . Based on the temporal co-release network of Top 100 musicians, we uncover a diverse community structure characterizing the electronic music industry.
Edit intent: clarity
Original:  We find that while this ranking list of popularity publishes the Top 100 names, only the top 20 is relatively stable in time, showcasing a lock-in effect on the stars of electronic music . Based on the temporal co-release network of Top 100 musicians, we uncover a diverse community structure characterizing the electronic music industry.
Revised:  We find that while this ranking list of popularity publishes the Top 100 names, only the top 20 is relatively stable in time, showcasing a lock-in effect on the stars of electronic music . Based on the temporal co-release network of top musicians, we uncover a diverse community structure characterizing the electronic music industry.
Edit intent: fluency
Original:  We find that while this ranking list of popularity publishes the Top 100 names, only the top 20 is relatively stable in time, showcasing a lock-in effect on the stars of electronic music . Based on the temporal co-release network of Top 100 musicians, we uncover a diverse community structure characterizing the electronic music industry.
Revised:  We find that while this ranking list of popularity publishes the Top 100 names, only the top 20 is relatively stable in time, showcasing a lock-in effect on the stars of electronic music . Based on the temporal co-release network of Top 100 musicians, we extract a diverse community structure characterizing the electronic music industry.
Edit intent: clarity
Original:  These groups of artists are temporally segregated, formed one after the other around leading musicians, and represent slight changes in music genres.
Revised:  These groups of artists are temporally segregated, sequentially formed around leading musicians, and represent slight changes in music genres.
Edit intent: clarity
Original:  These groups of artists are temporally segregated, formed one after the other around leading musicians, and represent slight changes in music genres.
Revised:  These groups of artists are temporally segregated, formed one after the other around leading musicians, and represent changes in musical genres.
Edit intent: clarity
Original:  We show that a major building force behind such communities is mentorship: around half of the musicians entering the Top 100 have been mentored by current leading figures before they entered the Top 100.
Revised:  We show that a major driving force behind the formation of music communities is mentorship: around half of the musicians entering the Top 100 have been mentored by current leading figures before they entered the Top 100.
Edit intent: clarity
Original:  We show that a major building force behind such communities is mentorship: around half of the musicians entering the Top 100 have been mentored by current leading figures before they entered the Top 100.
Revised:  We show that a major building force behind such communities is mentorship: around half of musicians entering the Top 100 have been mentored by current leading figures before they entered the Top 100.
Edit intent: fluency
Original:  We show that a major building force behind such communities is mentorship: around half of the musicians entering the Top 100 have been mentored by current leading figures before they entered the Top 100.
Revised:  We show that a major building force behind such communities is mentorship: around half of the musicians entering the top 100 have been mentored by current leading figures before they entered the Top 100.
Edit intent: fluency
Original:  We show that a major building force behind such communities is mentorship: around half of the musicians entering the Top 100 have been mentored by current leading figures before they entered the Top 100.
Revised:  We show that a major building force behind such communities is mentorship: around half of the musicians entering the Top 100 have been mentored by current leading figures before they entered the list.
Edit intent: clarity
Original:  We also find that the mentees are unlikely to break into the top 20, yet have much higher expected best ranks than those who were not mentored.
Revised:  We also find that mentees are unlikely to break into the top 20, yet have much higher expected best ranks than those who were not mentored.
Edit intent: clarity
Original: In this paper, we develop efficient methods for the computation of low multilinear rank approximations of tensors based on randomized algorithms.
Revised: In this paper, we focus on developing randomized algorithms for the computation of low multilinear rank approximations of tensors based on randomized algorithms.
Edit intent: clarity
Original:  Combining the random projection with the singular value decomposition , the rank-revealing QR decomposition and the rank-revealing LU factorization, respectively, we obtain three randomized algorithms for computing the low multilinear rank approximations.
Revised:  Combining the random projection and the singular value decomposition , the rank-revealing QR decomposition and the rank-revealing LU factorization, respectively, we obtain three randomized algorithms for computing the low multilinear rank approximations.
Edit intent: fluency
Original:  Based on the singular values of sub-Gaussian matrices, we derive the error bounds for each algorithmwith probability.
Revised:  Based on the singular values of sub-Gaussian matrices, we make a probabilistic analysis for the error bounds for each algorithmwith probability.
Edit intent: clarity
Original: Cooperative or collective perception (or sensing) enables connected and automated vehicles to exchange sensor information to improve their perception of the driving environment.
Revised: Connected and Automated Vehicles (CAVs) utilize a variety of onboard sensors to sense their surrounding environment. CAVs can improve their perception capabilities if vehicles exchange information about what they sense using V2X communications. This is known as cooperative or collective perception (or sensing) enables connected and automated vehicles to exchange sensor information to improve their perception of the driving environment.
Edit intent: clarity
Original:  This study shows that current collective perception message generation rules generate a high number of  messages with information about a small number of detected vehicles .
Revised:  This study shows that current collective perception message generation rules generate a high number of collective perception messages with information about a small number of detected vehicles .
Edit intent: fluency
Original:  This study shows that current collective perception message generation rules generate a high number of  messages with information about a small number of detected vehicles .
Revised:  This study shows that current collective perception message generation rules generate a high number of messages with information about a small number of detected objects .
Edit intent: clarity
Original:  This results in an inefficient utilization of the communication channel that reduces the effectiveness of collective perception.
Revised:  This results in an inefficient use of the communication channel that reduces the effectiveness of collective perception.
Edit intent: clarity
Original:  This study proposes a novel algorithm that modifies how the information of detected vehicles is organized in collective perception messages.
Revised:  This study proposes a novel algorithm that modifies the generation of collective perception messages.
Edit intent: clarity
Original:  The proposed algorithm improves the V2X (Vehicle to Everything) reliability and the perception compared to current ETSI solutions for collective perception or cooperative sensing .
Revised:  We demonstrate that the proposed solution improves the reliability of V2X (Vehicle to Everything) reliability and the perception compared to current ETSI solutions for collective perception or cooperative sensing .
Edit intent: clarity
Original:  The proposed algorithm improves the V2X (Vehicle to Everything) reliability and the perception compared to current ETSI solutions for collective perception or cooperative sensing .
Revised:  The proposed algorithm improves the V2X communication and the perception compared to current ETSI solutions for collective perception or cooperative sensing .
Edit intent: clarity
Original:  We show that the number of compacted binary trees of size n is asymptotically given by \Theta\left( n! \, 4^n e^{3a_1n^{1/3}} n^{3/4} \right), where a_1\approx-2.
Revised:  We show that the number of compacted binary trees of size n grows asymptotically like \Theta\left( n! \, 4^n e^{3a_1n^{1/3}} n^{3/4} \right), where a_1\approx-2.
Edit intent: clarity
Original:  Our method involves a new two parameter recurrence which yields an algorithm of quadratic arithmetic complexity for computing the number of compact trees of a given size .
Revised:  Our method involves a new two parameter recurrence which yields an algorithm of quadratic arithmetic complexity .
Edit intent: clarity
Original:  Using ^{13 the contributions of different metabolic pathways to this production and secretion of citrate could be identified .
Revised:  With the application of ^{13 the contributions of different metabolic pathways to this production and secretion of citrate could be identified .
Edit intent: clarity
Original:  Using ^{13 the contributions of different metabolic pathways to this production and secretion of citrate could be identified .
Revised:  Using ^{13 the contributions of different metabolic pathways to this production and secretion of citrate .
Edit intent: clarity
Original:  In this work we present a probabilistic model describing the production and secretion of citrate in the mitochondria of prostatic epithelial cells  .
Revised:  In this work we present a probabilistic model describing the mitochondrial production and the secretion of citrate in the mitochondria of prostatic epithelial cells .
Edit intent: fluency
Original:  In this work we present a probabilistic model describing the production and secretion of citrate in the mitochondria of prostatic epithelial cells  .
Revised:  In this work we present a probabilistic model describing the production and secretion of citrate by prostatic epithelial cells .
Edit intent: clarity
Original:  This measure is independent of initial ^{13}C-enrichment of the administered supplements and of ^{13}C J-coupling patterns, making this method robust also if SNR is low.
Revised:  These measures are independent of initial ^{13}C-enrichment of the administered supplements and of ^{13}C J-coupling patterns, making this method robust also if SNR is low.
Edit intent: fluency
Original:  We propose that these equations can be used to distinguish between citrate metabolism in healthy prostate tissue cells and in malignant cells, or they can be used to follow changes in citrate metabolism during the process towards malignancy .
Revised:  We propose that these equations can be used to distinguish between citrate metabolism in healthy and diseased prostate tissue, in particular upon malignant transformation .
Edit intent: clarity
Original:  This has been previously considered in a series of  works by Tao and Vu, and our results improve upon theirs in two ways: (i) We are able to handle \|M\| = O(\exp(n^{c})), whereas the results of Tao and Vu are applicable only for M = O(poly(n)).
Revised:  This has been previously considered in a series of influential works by Tao and Vu, and our results improve upon theirs in two ways: (i) We are able to handle \|M\| = O(\exp(n^{c})), whereas the results of Tao and Vu are applicable only for M = O(poly(n)).
Edit intent: clarity
Original:  (ii) Even for M = O(poly(n)), we are able to extract more refined information -- for instance, our results show that for such M, the probability that M_n is singular is O(\exp(-n^{c})), whereas even in the case when \xi is a Bernoulli random variable, the results of Tao and Vu  give a bound of the form O_{C}(n^{-C}) for any constant C>0.
Revised:  (ii) Even for M = O(poly(n)), we are able to extract more refined information -- for instance, our results show that for such M, the probability that M_n is singular is O(\exp(-n^{c})), whereas even in the case when \xi is a Bernoulli random variable, the results of Tao and Vu only give a bound of the form O_{C}(n^{-C}) for any constant C>0.
Edit intent: clarity
Original:  The main technical novelty of the present work, and the reason for the quantitative improvements, is that unlike all previous works on this problem, we completely avoid the use of the inverse Littlewood-Offord theorems .
Revised:  As opposed to all previous works on this problem, we completely avoid the use of the inverse Littlewood-Offord theorems .
Edit intent: coherence
Original:  Instead, we utilize and extend a combinatorial approach to random matrix theory , recently developed by the author along with Ferber, Luh, and Samotij .
Revised:  Instead, we utilize and extend a combinatorial approach to random matrix theory , recently developed by Ferber, Luh, and Samotij .
Edit intent: clarity
Original:  Instead, we utilize and extend a combinatorial approach to random matrix theory , recently developed by the author along with Ferber, Luh, and Samotij .
Revised:  Instead, we utilize and extend a combinatorial approach to random matrix theory , recently developed by the author along with Ferber, Luh, Samotij, and the author .
Edit intent: coherence
Original: Identifying influential spreaders in the complex network has been a hot topic in the study of network characteristic.
Revised: The identification of influential spreaders in the complex network has been a hot topic in the study of network characteristic.
Edit intent: fluency
Original:  Lots of centrality measures have been proposed to address this problem, but most methods have their own limitationsand shortcomings .
Revised:  Lots of centrality measures have been proposed to address this problem, but most have limitations .
Edit intent: clarity
Original:  In this paper, a novel method is proposed to identify influencers in complex networks via the local information dimension.
Revised:  In this paper, a method for identifying influencers in complex networks via the local information dimension.
Edit intent: clarity
Original:  This proposed method considers the local structure property around the central node , so the scale of locality only increases to half of the maximum value of the shortest distance from the central node.
Revised:  This proposed method considers the local structural properties around the central node , so the scale of locality only increases to half of the maximum value of the shortest distance from the central node.
Edit intent: fluency
Original:  This proposed method considers the local structure property around the central node , so the scale of locality only increases to half of the maximum value of the shortest distance from the central node.
Revised:  This proposed method considers the local structure property around the central node ; therefore, the scale of locality only increases to half of the maximum value of the shortest distance from the central node.
Edit intent: coherence
Original:  Thus this proposed method considers the quasi-local information and reduces the computational complexity.
Revised:  Thus , the proposed method considers the quasi-local information and reduces the computational complexity.
Edit intent: clarity
Original:  Thus this proposed method considers the quasi-local information and reduces the computational complexity.
Revised:  Thus this proposed method considers the quasilocal information and reduces the computational complexity.
Edit intent: fluency
Original:  The information (number of nodes) in boxes is considered by Shannon entropy, which is more reasonable.
Revised:  The information (number of nodes) in boxes is described via the Shannon entropy, which is more reasonable.
Edit intent: clarity
Original:  The node would be more influential when the local information dimension of this node is higher.
Revised:  A node is more influential when the local information dimension of this node is higher.
Edit intent: clarity
Original:  The node would be more influential when the local information dimension of this node is higher.
Revised:  The node would be more influential when its local information dimensionality is higher.
Edit intent: clarity
Original:  In order to show the effectiveness of this proposed method, five exiting centrality measures are used as comparison methods to rank influential nodes in six real-world complex networks.
Revised:  In order to show the effectiveness of the proposed method, five exiting centrality measures are used as comparison methods to rank influential nodes in six real-world complex networks.
Edit intent: clarity
Original:  In order to show the effectiveness of this proposed method, five exiting centrality measures are used as comparison methods to rank influential nodes in six real-world complex networks.
Revised:  In order to show the effectiveness of this proposed method, five existing centrality measures are used as comparison methods to rank influential nodes in six real-world complex networks.
Edit intent: fluency
Original:  In order to show the effectiveness of this proposed method, five exiting centrality measures are used as comparison methods to rank influential nodes in six real-world complex networks.
Revised:  In order to show the effectiveness of this proposed method, five exiting centrality measures are used as comparison methods to rank influential nodes in six real world complex networks.
Edit intent: fluency