wanyu/IteraTeR_v2 huggingface dataset:
Original: In this paper, we present a quantum heuristic approach to solve the subset-sum problem on quantum computers . Under described certain assumptions, we show that the approach is able to yield the exact solution in polynomial time and may provide exponential speed-up over the classical algorithms  .
Revised: In this paper, we present a quantum heuristic approach to solve the subset-sum problem on quantum computers . Under described certain assumptions, we show that the exact solution of the subset sum problem my be obtained in polynomial time and may provide exponential speed-up over the classical algorithms .
Edit intent: clarity
Original: In this paper, we present a quantum heuristic approach to solve the subset-sum problem on quantum computers . Under described certain assumptions, we show that the approach is able to yield the exact solution in polynomial time and may provide exponential speed-up over the classical algorithms  .
Revised: In this paper, we present a quantum heuristic approach to solve the subset-sum problem on quantum computers . Under described certain assumptions, we show that the approach is able to yield the exact solution in polynomial time and the exponential speed-up over the classical algorithms .
Edit intent: clarity
Original:  The computation of the parameter sensitivities  poses many computational challenges when taking stochastic noise into account.
Revised:  The computation of the parameter sensitivities , however, poses many computational challenges when taking stochastic noise into account.
Edit intent: coherence
Original:  This paper proposes a new efficient finite difference method for computing parameter sensitivities of biochemical reactions.
Revised:  This paper proposes a new finite difference method for computing parameter sensitivities of biochemical reactions.
Edit intent: clarity
Original:  This paper proposes a new efficient finite difference method for computing parameter sensitivities of biochemical reactions.
Revised:  This paper proposes a new efficient finite difference method for efficiently computing sensitivities of biochemical reactions.
Edit intent: clarity
Original:  We employ propensity bounds of reactions to simulate the nominal and perturbed processes and build the estimator .
Revised:  We employ propensity bounds of reactions to couple the simulation of the nominal and perturbed processes and build the estimator .
Edit intent: clarity
Original:  We employ propensity bounds of reactions to simulate the nominal and perturbed processes and build the estimator .
Revised:  We employ propensity bounds of reactions to simulate the nominal and perturbed processes .
Edit intent: clarity
Original: We propose a recurrent extension of the Ladder network, which is motivated by the inference required in hierarchical latent variable models.
Revised: We propose a recurrent extension of the Ladder networks whose structure is motivated by the inference required in hierarchical latent variable models.
Edit intent: clarity
Original:  The results suggest that the proposed architecture and principles are powerful tools for learning a hierarchy of abstractions,  handling temporal information , modeling relations and interactions between objects .
Revised:  The results suggest that the proposed architecture and principles are powerful tools for learning a hierarchy of abstractions, handling temporal information .
Edit intent: clarity
Original:  Using this theory, known as super-statistics , we identify taxonomic orders as largely autonomous evolutionary units, each likely experiencing its own unique and conserved region of an adaptive landscape.
Revised:  Using this theory, known as superstatistics , we identify taxonomic orders as largely autonomous evolutionary units, each likely experiencing its own unique and conserved region of an adaptive landscape.
Edit intent: fluency
Original:  Compared to other approaches that have used simple birth-death processes, equilibrial dynamics  or non-linear theories from complexity science, super-statistics is superior in its ability to account for both small and extreme fluctuations in fossil diversity.
Revised:  Compared to other approaches that have used simple birth-death processes, equilibrial dynamics , or non-linear theories from complexity science, super-statistics is superior in its ability to account for both small and extreme fluctuations in fossil diversity.
Edit intent: fluency
Original:  Its success opens up new research directions to better understand the universal nature of non-equilibrium dynamics across disparate systems of interest---from societal to physical to biological.
Revised:  Its success opens up new research directions to better understand the universal nature of non-equilibrium dynamics across disparate systems of interest--from societal to physical to biological.
Edit intent: fluency
Original: Fluctuations in biodiversity, both large and small, are pervasive through the fossil record, yet we do not understand the processes generating them.
Revised: Fluctuations in biodiversity, large and small, are pervasive through the fossil record, yet we do not understand the processes generating them.
Edit intent: clarity
Original: Fluctuations in biodiversity, both large and small, are pervasive through the fossil record, yet we do not understand the processes generating them.
Revised: Fluctuations in biodiversity, both large and small, are pervasive in the fossil record, yet we do not understand the processes generating them.
Edit intent: clarity
Original:  Here we use a novel extension of theory from non-equilibrium statistical physics to show that three universal properties of macroevolution--(i) heterogeneity of diversification rates between taxa, likely driven by (ii) niche conservatism and (iii) punctuated adaptive radiation--are sufficient to explain the previously unaccounted for fat-tailed form of fluctuations in diversity through the Phanerozoic.
Revised:  Here we extend theory from non-equilibrium statistical physics to show that three universal properties of macroevolution--(i) heterogeneity of diversification rates between taxa, likely driven by (ii) niche conservatism and (iii) punctuated adaptive radiation--are sufficient to explain the previously unaccounted for fat-tailed form of fluctuations in diversity through the Phanerozoic.
Edit intent: clarity
Original:  Here we use a novel extension of theory from non-equilibrium statistical physics to show that three universal properties of macroevolution--(i) heterogeneity of diversification rates between taxa, likely driven by (ii) niche conservatism and (iii) punctuated adaptive radiation--are sufficient to explain the previously unaccounted for fat-tailed form of fluctuations in diversity through the Phanerozoic.
Revised:  Here we use a novel extension of theory from non-equilibrium statistical physics to describe the previously unaccounted for fat-tailed form of fluctuations in diversity through the Phanerozoic.
Edit intent: clarity
Original:  Here we use a novel extension of theory from non-equilibrium statistical physics to show that three universal properties of macroevolution--(i) heterogeneity of diversification rates between taxa, likely driven by (ii) niche conservatism and (iii) punctuated adaptive radiation--are sufficient to explain the previously unaccounted for fat-tailed form of fluctuations in diversity through the Phanerozoic.
Revised:  Here we use a novel extension of theory from non-equilibrium statistical physics to show that three universal properties of macroevolution--(i) heterogeneity of diversification rates between taxa, likely driven by (ii) niche conservatism and (iii) punctuated adaptive radiation--are sufficient to explain the previously unaccounted for fat-tailed form of fluctuations in marine invertebrate richness through the Phanerozoic.
Edit intent: clarity
Original:  while between-order diversification is non-equilibrial , driven by major evolutionary innovations . Compared to other approaches that have used simple birth-death processes,  equilibrial dynamics, or non-linear theories from complexity science, super-statistics is superior in its ability to account for both small and extreme fluctuations in fossil diversity .
Revised:  while between-clade diversification is non-equilibrial , driven by major evolutionary innovations . Compared to other approaches that have used simple birth-death processes, equilibrial dynamics, or non-linear theories from complexity science, super-statistics is superior in its ability to account for both small and extreme fluctuations in fossil diversity .
Edit intent: clarity
Original:  while between-order diversification is non-equilibrial , driven by major evolutionary innovations . Compared to other approaches that have used simple birth-death processes,  equilibrial dynamics, or non-linear theories from complexity science, super-statistics is superior in its ability to account for both small and extreme fluctuations in fossil diversity .
Revised:  while between-order diversification is non-equilibrial , driven by major evolutionary innovations . Compared to other approaches that have used simple birth-death processes, simple equilibrial dynamics, or non-linear theories from complexity science, super-statistics is superior in its ability to account for both small and extreme fluctuations in fossil diversity .
Edit intent: fluency
Original:  while between-order diversification is non-equilibrial , driven by major evolutionary innovations . Compared to other approaches that have used simple birth-death processes,  equilibrial dynamics, or non-linear theories from complexity science, super-statistics is superior in its ability to account for both small and extreme fluctuations in fossil diversity .
Revised:  while between-order diversification is non-equilibrial , driven by major evolutionary innovations . Compared to other approaches that have used simple birth-death processes, equilibrial dynamics, or non-linear theories from complexity science, superstatistics is superior in its ability to account for both small and extreme fluctuations in fossil diversity .
Edit intent: fluency
Original:  while between-order diversification is non-equilibrial , driven by major evolutionary innovations . Compared to other approaches that have used simple birth-death processes,  equilibrial dynamics, or non-linear theories from complexity science, super-statistics is superior in its ability to account for both small and extreme fluctuations in fossil diversity .
Revised:  while between-order diversification is non-equilibrial , driven by major evolutionary innovations . Compared to other approaches that have used simple birth-death processes, equilibrial dynamics, or non-linear theories from complexity science, super-statistics is superior in its ability to account for both small and extreme fluctuations in the richness of fossil taxa .
Edit intent: clarity
Original:  Specifically in the biological case, research is motivated to understand the evolutionary processes leading to the stasis of order-level occupancy in an adaptive landscape punctuated by innovations between orders .
Revised:  Specifically in the biological case, research is motivated to understand the evolutionary processes leading to stasis in an adaptive landscape punctuated by innovations between orders .
Edit intent: clarity
Original:  and (2) to improve computational performance, we provide a different mechanism for choosing which ensembles should be included in the multi-level algorithm.
Revised:  and (2) to improve computational performance, we demonstrate the successful use of a different mechanism for choosing which ensembles should be included in the multi-level algorithm.
Edit intent: clarity
Original:  This autonomous management vision has to be extended to the end to end network , to satisfy 5G network management requirements .
Revised:  To satisfy 5G network management requirements, this autonomous management vision has to be extended to the end to end network , to satisfy 5G network management requirements .
Edit intent: fluency
Original:  This autonomous management vision has to be extended to the end to end network , to satisfy 5G network management requirements .
Revised:  This autonomous management vision has to be extended to the end to end network .
Edit intent: clarity
Original:  In this paper  we survey how network management can significantly benefit from ML solutions.
Revised:  In this paper , we survey how network management can significantly benefit from ML solutions.
Edit intent: fluency
Original:  We review and provide the basic concepts and taxonomy for SON, network management and ML. We analyse the available state of the art in the literature, standardization  and in the market.
Revised:  We review and provide the basic concepts and taxonomy for SON, network management and ML. We analyse the available state of the art in the literature, standardization , and in the market.
Edit intent: fluency
Original:  We pay special attention to  3GPP  evolution in the area of network management and to the data that can be extracted from 3GPP networks, in order to gain knowledge and experience in how the network is working, and improve network performance in a proactive way.
Revised:  We pay special attention to 3GPP ) evolution in the area of network management and to the data that can be extracted from 3GPP networks, in order to gain knowledge and experience in how the network is working, and improve network performance in a proactive way.
Edit intent: fluency
Original:  Finally, we go through the main challenges associated with this research line , in both 4G and in what 5G is getting designed, while identifying new directions for research.
Revised:  Finally, we go through the main challenges associated with this line of research , in both 4G and in what 5G is getting designed, while identifying new directions for research.
Edit intent: fluency
Original: Graphs provide a natural mathematical abstraction for systems with pairwise interactions, and thus have become a prevalent tool for the representation of systems across various scientific domains.
Revised: Graphs provide a natural mathematical abstraction for systems with pairwise interactions, and thus have become a prevalent tool across various scientific domains.
Edit intent: clarity
Original:  However, as  the size of relational datasets continues to grow, traditional graph-based approaches are increasingly replaced by other modeling paradigms, which enable a more flexible treatment of such datasets . A promising framework in this context is provided by graphons, which have been formally introduced as the natural limiting objects for graphs of increasing sizes.
Revised:  However, as the size of relational datasets continues to grow, traditional graph-based approaches are increasingly replaced by more flexible modeling paradigms . A promising framework in this context is provided by graphons, which have been formally introduced as the natural limiting objects for graphs of increasing sizes.
Edit intent: clarity
Original:  However, as  the size of relational datasets continues to grow, traditional graph-based approaches are increasingly replaced by other modeling paradigms, which enable a more flexible treatment of such datasets . A promising framework in this context is provided by graphons, which have been formally introduced as the natural limiting objects for graphs of increasing sizes.
Revised:  However, as the size of relational datasets continues to grow, traditional graph-based approaches are increasingly replaced by other modeling paradigms, which enable a more flexible treatment of such datasets . A promising framework in this regard is that of graphons, which have been formally introduced as the natural limiting objects for graphs of increasing sizes.
Edit intent: clarity
Original:  We further establish concentration inequalities showing that these centrality functions are natural limits of their analogous counterparts defined on sequences of random graphs of increasing size.
Revised:  We further establish concentration inequalities showing that these centrality functions arise naturally as limits of their analogous counterparts defined on sequences of random graphs of increasing size.
Edit intent: clarity
Original:  We discuss several strategies for computing these centrality measures, and illustrate them through a set of numerical examples .
Revised:  We discuss several strategies for computing graphon centrality functions and illustrate the aforementioned concentration inequalities through numerical experiments .
Edit intent: clarity
Original:  A key motivation for closing this gap is that centrality measures defined at the modeling level of graphons will be inherently robust to stochastic variations of specific graph realizations.
Revised:  A key advantage of this approach is that centrality measures defined at the modeling level of graphons will be inherently robust to stochastic variations of specific graph realizations.
Edit intent: clarity
Original:  A key motivation for closing this gap is that centrality measures defined at the modeling level of graphons will be inherently robust to stochastic variations of specific graph realizations.
Revised:  A key motivation for closing this gap is that centrality measures defined at the modeling level of graphons are inherently robust to stochastic variations of specific graph realizations.
Edit intent: coherence
Original:  In particular, we build on the theory of linear integral operators to define degree, eigenvector, and Katz centrality functions for graphons .
Revised:  In particular, we build on the theory of linear integral operators , we define degree, eigenvector, and Katz centrality functions for graphons .
Edit intent: fluency
Original:  We further establish concentration inequalities showing that these centrality functions arise naturally as limits of their analogous counterparts defined on sequences of converging graphs of increasing size.
Revised:  We further establish concentration inequalities showing that these centrality functions arise naturally as limits of their counterparts defined on sequences of converging graphs of increasing size.
Edit intent: clarity
Original:  We further establish concentration inequalities showing that these centrality functions arise naturally as limits of their analogous counterparts defined on sequences of converging graphs of increasing size.
Revised:  We further establish concentration inequalities showing that these centrality functions arise naturally as limits of their analogous counterparts defined on sequences of graphs of increasing size.
Edit intent: clarity
Original:  Moreover, we provide high-probability bounds on the distance between the graphon centrality function and the centrality measures realized in any sampled graph .
Revised:  Moreover, we provide high-probability bounds between the graphon centrality function and the centrality measures realized in any sampled graph .
Edit intent: clarity
Original:  Moreover, we provide high-probability bounds on the distance between the graphon centrality function and the centrality measures realized in any sampled graph .
Revised:  Moreover, we provide high-probability bounds on the distance between the graphon centrality functions and the centrality measures realized in any sampled graph .
Edit intent: fluency
Original:  Moreover, we provide high-probability bounds on the distance between the graphon centrality function and the centrality measures realized in any sampled graph .
Revised:  Moreover, we provide high-probability bounds on the distance between the graphon centrality function and the centrality measures on any sampled graph .
Edit intent: clarity
Original:  The same concentration inequalities also provide high-probability bounds between the graphon centrality functions and the centrality measures on any sampled graph, thereby establishing a measure of uncertainty of the measured centrality score. 
Revised:  The same concentration inequalities also provide high-probability bounds between the graphon centrality functions and the centrality measures on any sampled graph, thereby establishing a measure of uncertainty of the measured centrality score. The same concentration inequalities also provide high-probability bounds between the graphon centrality functions and the centrality measures on any sampled graph, thereby establishing a measure of uncertainty of the measured centrality score.
Edit intent: fluency
Original:  While the capsid structures are well-characterized for most viruses, the structure of RNA inside the shells and the factors contributing to it remain poorly understood.
Revised:  While the capsid structures are well characterized for most viruses, the structure of RNA inside the shells and the factors contributing to it remain poorly understood.
Edit intent: fluency
Original:  We study the impact of base-pairing on the conformations of RNA and find that it undergoes a swollen coil to globule continuous transition as a function of the strength of the pairing interaction.
Revised:  We study the impact of base pairing on the conformations of RNA and find that it undergoes a swollen coil to globule continuous transition as a function of the strength of the pairing interaction.
Edit intent: fluency
Original: As network science has matured as a well-established field of research, there are already a number of courses on this topic developed and offered at various higher education institutions, often at postgraduate levels.
Revised: As network science has matured as an established field of research, there are already a number of courses on this topic developed and offered at various higher education institutions, often at postgraduate levels.
Edit intent: clarity
Original:  In those courses, instructors have adopted different approaches with different focus areas and curricular designs.
Revised:  In those courses, instructors adopted different approaches with different focus areas and curricular designs.
Edit intent: clarity
Original:  Community detection in the topic network revealed seven topic clusters, which had a reasonable matching with the concept list previously generated by students and educators through the Network Literacy initiative.
Revised:  Community detection in the topic network revealed seven topic clusters, which matched reasonably with the concept list previously generated by students and educators through the Network Literacy initiative.
Edit intent: clarity
Original:  These results illustrate the current state of the consensus formed among the network science community on what should be taught about networks and how, which may also be informative for K-12 education and informal education.
Revised:  These results illustrate the current state of the consensus formed among the network science community on what should be taught about networks and how, which may also be informative for K--12 education and informal education.
Edit intent: fluency
Original:  Specifically , we show that if n requests are assigned to n serversbased on the proposed coded scheme , the maximum load of servers will be \Theta(1), while in the nearest replica strategy the maximum load is \Theta(\log n) . More surprisingly, this coded scheme will have the same communication cost performance as the nearest replica strategy, asymptotically.
Revised:  Here , we show that if n requests are assigned to n serversbased on the proposed coded scheme , the maximum load of servers will be \Theta(1), while in the nearest replica strategy the maximum load is \Theta(\log n) . More surprisingly, this coded scheme will have the same communication cost performance as the nearest replica strategy, asymptotically.
Edit intent: fluency