wanyu/IteraTeR_v2 huggingface dataset:
Original: A construction method for duplex cage structures with icosahedral symmetry made out of a single-stranded RNA or DNA molecule is presented and applied to an icosidodecahedral cage.
Revised: A construction method for duplex cage structures with icosahedral symmetry made out of a single-stranded DNA molecules is presented and applied to an icosidodecahedral cage.
Edit intent: clarity
Original:  The emphasis is put on minimizing stress caused on the final structure by supercoiling of the strands, while optimising rigidity of the vertices.
Edit intent: coherence
Original:  This is hence the first blueprint for the organisation of a cage structure with a noncrystallographic symmetry that involves rigid vertex configurations throughout, and may therefore assist in the design of containers from DNA or RNA for applications in nanotechnology.
Revised:  This is hence the first blueprint for the organisation of a cage structure with a noncrystallographic symmetry may assist in the design of containers from DNA or RNA for applications in nanotechnology.
Edit intent: coherence
Original:  This is hence the first blueprint for the organisation of a cage structure with a noncrystallographic symmetry that involves rigid vertex configurations throughout, and may therefore assist in the design of containers from DNA or RNA for applications in nanotechnology.
Revised:  This is hence the first blueprint for the organisation of a cage structure with a noncrystallographic symmetry that involves rigid vertex configurations throughout, and may therefore assist in the design of containers made from DNA for applications in nanotechnology.
Edit intent: clarity
Original:  Fractal dimension, microvascular density (MVD), blood flow and shear force has been computed for a wide range of parameters and found to be in good agreement with experimental data from human and mouse melanoma .
Revised:  Fractal dimension, microvascular density (MVD), blood flow and shear force has been computed for a wide range of parameters .
Edit intent: clarity
Original: The other main novelty of our algorithm  is an analysis showing that its running time is bounded only in terms of the condition number of the problem instance  .
Revised: The other main novelty of our algorithm , is an analysis showing that its running time is bounded only in terms of the condition number of the problem instance .
Edit intent: fluency
Original: The other main novelty of our algorithm  is an analysis showing that its running time is bounded only in terms of the condition number of the problem instance  .
Revised: The other main novelty of our algorithm is an analysis showing that its running time is bounded in terms of the condition number of the problem instance .
Edit intent: clarity
Original:  The effective temperature takes a higher value than the temperature of the bath when the effect of the motors is not correlated with the structural rearrangements they induce.
Revised:  The effective temperature takes a value which is higher than the temperature of the bath when the effect of the motors is not correlated with the structural rearrangements they induce.
Edit intent: clarity
Original:  The objective is to design a sensing policy for channel selection to maximize the average reward  .
Revised:  The problem is to design a sensing policy for channel selection to maximize the average reward .
Edit intent: clarity
Original:  We show that the myopic sensing policy has a simple robust structure that reduces channel selection to a counting procedure and obviates the need for knowing the channel transition probabilities.
Revised:  We show that the myopic sensing policy has a simple robust structure that reduces channel selection to a round-robin procedure and obviates the need for knowing the channel transition probabilities.
Edit intent: clarity
Original:  The optimality of this simple policy is established for the two-channel case and conjectured for the general case based on extensive simulations .
Revised:  The optimality of this simple policy is established for the two-channel case and conjectured for the general case based on numerical results .
Edit intent: clarity
Original:  These results apply to cognitive radio networks for spectrum overlay , opportunistic transmission in fading environments, and resource-constrained jamming and anti-jamming.
Revised:  These results apply to cognitive radio networks , opportunistic transmission in fading environments, and resource-constrained jamming and anti-jamming.
Edit intent: clarity
Original: This paper presents a new upper bound of the number of Hamiltonian cycles on a symmetric diagraph , which is tighter than the famous Minc's bound and a refiner of Bre gmman 's bound.
Revised: An upper bound of the number of Hamiltonian cycles on a symmetric diagraph , which is tighter than the famous Minc's bound and a refiner of Bre gmman 's bound.
Edit intent: clarity
Original: This paper presents a new upper bound of the number of Hamiltonian cycles on a symmetric diagraph , which is tighter than the famous Minc's bound and a refiner of Bre gmman 's bound.
Revised: This paper presents a new upper bound of the number of Hamiltonian cycles on a symmetric diagraph , which is tighter than the classics Minc's bound and a refiner of Bre gmman 's bound.
Edit intent: fluency
Original: This paper presents a new upper bound of the number of Hamiltonian cycles on a symmetric diagraph , which is tighter than the famous Minc's bound and a refiner of Bre gmman 's bound.
Revised: This paper presents a new upper bound of the number of Hamiltonian cycles on a symmetric diagraph , which is tighter than the famous Minc's bound and Bre gmman 's bound.
Edit intent: clarity
Original: This paper presents a new upper bound of the number of Hamiltonian cycles on a symmetric diagraph , which is tighter than the famous Minc's bound and a refiner of Bre gmman 's bound.
Revised: This paper presents a new upper bound of the number of Hamiltonian cycles on a symmetric diagraph , which is tighter than the famous Minc's bound and a refiner of Bre gman 's bound.
Edit intent: fluency
Original:  A transformation from the problem ofcounting the number of Hamiltonian cycles of a undirected graph to that of counting the number of Hamiltonian cycles of a symmetric directed graph is also proposed .
Revised:  A transformation is proposed, so that counting the number of Hamiltonian cycles of a undirected graph to that of counting the number of Hamiltonian cycles of a symmetric directed graph is also proposed .
Edit intent: clarity
Original:  A transformation from the problem ofcounting the number of Hamiltonian cycles of a undirected graph to that of counting the number of Hamiltonian cycles of a symmetric directed graph is also proposed .
Revised:  A transformation from the problem ofcounting the number of Hamiltonian cycles of an undirected graph can be obtained by counting the number of Hamiltonian cycles of a symmetric directed graph is also proposed .
Edit intent: clarity
Original:  A transformation from the problem ofcounting the number of Hamiltonian cycles of a undirected graph to that of counting the number of Hamiltonian cycles of a symmetric directed graph is also proposed .
Revised:  A transformation from the problem ofcounting the number of Hamiltonian cycles of a undirected graph to that of counting the number of Hamiltonian cycles of a symmetric directed graph . In this way, an upper bound of the number of Hamiltonian cycles of undirected graphs is obtained .
Edit intent: clarity
Original: An upper bound of the number of Hamiltonian cycles of symmetric diagraphs is given in this paper, which is tighter than the classics Minc's bound and  Bregman's bound.
Revised: An upper bound for the number of Hamiltonian cycles of symmetric diagraphs is given in this paper, which is tighter than the classics Minc's bound and Bregman's bound.
Edit intent: fluency
Original: An upper bound of the number of Hamiltonian cycles of symmetric diagraphs is given in this paper, which is tighter than the classics Minc's bound and  Bregman's bound.
Revised: An upper bound of the number of Hamiltonian cycles of symmetric diagraphs is given in this paper, which is tighter than the classics Minc's bound and the Bregman's bound.
Edit intent: fluency
Original:  A transformation  is proposed, so that counting the number of Hamiltonian cycles of an undirected graph can be obtained by counting the number of Hamiltonian cycles of its corresponding symmetric directed graph.
Revised:  A transformation on graphs is proposed, so that counting the number of Hamiltonian cycles of an undirected graph can be obtained by counting the number of Hamiltonian cycles of its corresponding symmetric directed graph.
Edit intent: clarity
Original:  A transformation  is proposed, so that counting the number of Hamiltonian cycles of an undirected graph can be obtained by counting the number of Hamiltonian cycles of its corresponding symmetric directed graph.
Revised:  A transformation is proposed, so that counting the number of Hamiltonian cycles of an undirected graph can be done by counting the number of Hamiltonian cycles of its corresponding symmetric directed graph.
Edit intent: clarity
Original:  In this way, an upper bound of the number of Hamiltonian cycles of undirected graphs is  obtained.
Revised:  In this way, an upper bound for the number of Hamiltonian cycles of undirected graphs is obtained.
Edit intent: fluency
Original:  In this way, an upper bound of the number of Hamiltonian cycles of undirected graphs is  obtained.
Revised:  In this way, an upper bound of the number of Hamiltonian cycles of undirected graphs is also obtained.
Edit intent: clarity
Original: An upper bound for the number of Hamiltonian cycles of symmetric diagraphs is established first in this paper, which is tighter than the classics Minc's bound and the Bregman's bound.
Revised: An upper bound for the number of Hamiltonian cycles of symmetric diagraphs is established first in this paper, which is tighter than the famous Minc's bound and the Bregman's bound.
Edit intent: fluency
Original: Identifying strongly connected substructures in large networks provides insight in their coarse-grained organization.
Revised: Identifying strongly connected substructures in large networks provides insight into their coarse-grained organization.
Edit intent: fluency
Original:  Several approaches based on the optimization of a quality function, e.g.  the modularity, have been proposed.
Revised:  Several approaches based on the optimization of a quality function, e.g. , the modularity, have been proposed.
Edit intent: fluency
Original:  We have developed a multi-step extension of the greedy algorithm (MSG) for modularity optimization and combined it with a simplistic refinement procedure called ``Vertex Mover'' (VM) which reassigns vertices to neighboring communities to improve the final modularity value.
Revised:  We present here a multistep extension of the greedy algorithm (MSG) for modularity optimization and combined it with a simplistic refinement procedure called ``Vertex Mover'' (VM) which reassigns vertices to neighboring communities to improve the final modularity value.
Edit intent: clarity
Original:  We have developed a multi-step extension of the greedy algorithm (MSG) for modularity optimization and combined it with a simplistic refinement procedure called ``Vertex Mover'' (VM) which reassigns vertices to neighboring communities to improve the final modularity value.
Revised:  We have developed a multi-step extension of the greedy algorithm (MSG) for modularity optimization and combined it with a simplistic refinement procedure called "vertex mover" (VM) which reassigns vertices to neighboring communities to improve the final modularity value.
Edit intent: fluency
Original:  We have developed a multi-step extension of the greedy algorithm (MSG) for modularity optimization and combined it with a simplistic refinement procedure called ``Vertex Mover'' (VM) which reassigns vertices to neighboring communities to improve the final modularity value.
Revised:  We have developed a multi-step extension of the greedy algorithm (MSG) for modularity optimization and combined it with a simplistic refinement procedure called ``Vertex Mover'' (VM) is used for reassigning vertices to neighboring communities to improve the final modularity value.
Edit intent: coherence
Original:  With an appropriate choice of the step-width in the MSG , the combined MSG VM algorithm is able to find solutions of higher modularity than those reported previously.
Revised:  With an appropriate choice of the step width , the combined MSG VM algorithm is able to find solutions of higher modularity than those reported previously.
Edit intent: clarity
Original:  With an appropriate choice of the step-width in the MSG , the combined MSG VM algorithm is able to find solutions of higher modularity than those reported previously.
Revised:  With an appropriate choice of the step-width in the MSG , the combined VM algorithm is able to find solutions of higher modularity than those reported previously.
Edit intent: fluency
Original:  The multi-step extension does not alter the running time expectation of the greedy algorithm .
Revised:  The multistep extension does not alter the running time expectation of the greedy algorithm .
Edit intent: fluency
Original:  Therefore, we conclude that the combined MSG VM algorithm yields network partitions of higher modularity in shorter time than reported previously .
Revised:  Therefore, we conclude that the combined MSG .
Edit intent: clarity
Original:  It uses both the geometrical organization of the data set and the available labels assigned to few points , giving additional information compared to unsupervised clustering methods.
Revised:  It uses both the geometrical organization of the data and the available labels assigned to few points , giving additional information compared to unsupervised clustering methods.
Edit intent: clarity
Original: In this paper will be introduced large, probably complete family of complex base systems, which are 'proper' - for each point of the space there is representation and is unique for all but some zero measure set.
Revised: In this paper will be introduced large, probably complete family of complex base systems, which are 'proper' - for each point of the space there is a representation which is unique for all but some zero measure set.
Edit intent: clarity
Original:  There will be introduced full methodology of analyzing and using this approach - both for the integer part: periodic lattice and the fractional: the attractor of some IFS, for which the convex hull or properties like dimension of the boundary can be found analytically.
Revised:  There will be introduced full methodology of analyzing and using this approach - both for the integer part: periodic lattice and the fractional: attractor of some IFS, for which the convex hull or properties like dimension of the boundary can be found analytically.
Edit intent: fluency
Original: This paper continues investigation of randomness-type properties emerging in idealized financial markets with continuous price processes.
Revised: This note continues investigation of randomness-type properties emerging in idealized financial markets with continuous price processes.
Edit intent: clarity
Original:  For the QC algorithm we show that the mean-squared error (m.s.e.) can be made arbitrarily small by tuning the link weight sequence, at a cost of the convergence rate .
Revised:  We show that the mean-squared error (m.s.e.) can be made arbitrarily small by tuning the link weight sequence, at a cost of the convergence rate .
Edit intent: coherence
Original:  For the QC algorithm we show that the mean-squared error (m.s.e.) can be made arbitrarily small by tuning the link weight sequence, at a cost of the convergence rate .
Revised:  For the QC algorithm we show that the meansquared error (m.s.e.) can be made arbitrarily small by tuning the link weight sequence, at a cost of the convergence rate .
Edit intent: fluency
Original:  The paper then focuses on constructing four-group ML decodable DSTBCs for application in the Jing-Hassibi protocol for cooperative diversity in synchronous wireless relay networks  .
Revised:  The paper then focuses on multi-group ML decodable DSTBCs for application in the Jing-Hassibi protocol for cooperative diversity in synchronous wireless relay networks .
Edit intent: clarity
Original:  The paper then focuses on constructing four-group ML decodable DSTBCs for application in the Jing-Hassibi protocol for cooperative diversity in synchronous wireless relay networks  .
Revised:  The paper then focuses on constructing four-group ML decodable DSTBCs for application in synchronous wireless relay networks .
Edit intent: clarity
Original: We analyze the asymptotic behavior of the sequence of random variables (x(n, x0))n \in N defined by x(0, x0) = x0 and x(n+1, x0) = A(n)x(n, x0), where (A(n))n \in N is a stationary and ergodic sequence of random matrices with entries in the semiring (R \cup -%DIFDELCMD < \infinity}%%% , max, +).
Revised: We analyze the asymptotic behavior of sequences of random variables (x(n, x0))n \in N defined by x(0, x0) = x0 and x(n+1, x0) = A(n)x(n, x0), where (A(n))n \in N is a stationary and ergodic sequence of random matrices with entries in the semiring (R \cup -%DIFDELCMD < \infinity}%%% , max, +).
Edit intent: fluency
Original: We analyze the asymptotic behavior of the sequence of random variables (x(n, x0))n \in N defined by x(0, x0) = x0 and x(n+1, x0) = A(n)x(n, x0), where (A(n))n \in N is a stationary and ergodic sequence of random matrices with entries in the semiring (R \cup -%DIFDELCMD < \infinity}%%% , max, +).
Revised: We analyze the asymptotic behavior of the sequence of random variables defined by an initial condition, a stationary and ergodic sequence of random matrices with entries in the semiring (R \cup -%DIFDELCMD < \infinity}%%% , max, +).
Edit intent: clarity
Original: We analyze the asymptotic behavior of the sequence of random variables (x(n, x0))n \in N defined by x(0, x0) = x0 and x(n+1, x0) = A(n)x(n, x0), where (A(n))n \in N is a stationary and ergodic sequence of random matrices with entries in the semiring (R \cup -%DIFDELCMD < \infinity}%%% , max, +).
Revised: We analyze the asymptotic behavior of the sequence of random variables (x(n, x0))n \in N defined by x(0, x0) = x0 and x(n+1, x0) = A(n)x(n, x0), where (A(n))n \in N is a stationary and ergodic sequence of random matrices with entries in the semiring (R \cup %DIFDELCMD < \infinity}%%% , max, +).
Edit intent: fluency
Original:  We give a necessary condition for 1/n x(n, x0) n \in N to converge almost-surely , which proves to be sufficient when the A(n) are i.i.d.
Revised:  We give a necessary condition for 1/n x(n, x0) n \in N to converge almost-surely , which proves to be sufficient when the matrices are i.i.d.
Edit intent: clarity
Original:  Moreover, we construct a new example, in which (A(n))n \in N is strongly mixing, that condition is satisfied, but 1/n x(n, x0) n \in N do not converge almost-surely .
Revised:  Moreover, we construct a new example, in which the sequence of matrices is strongly mixing, that condition is satisfied, but 1/n x(n, x0) n \in N do not converge almost-surely .
Edit intent: clarity
Original: Given a parametrization of a  plane algebraic curve C, some explicit adjoint linear systems on C are described in terms of determinants.
Revised: Given a parametrization of a plane algebraic curve C, some explicit adjoint pencils on C are described in terms of determinants.
Edit intent: clarity
Original:  We structure our analysis along three axes -- performance, availability and management -- and outline unmet database replication challenges at several levels.
Revised:  We structure our analysis along three axes : performance, availability and management -- and outline unmet database replication challenges at several levels.
Edit intent: fluency
Original:  We sift through  the last decade of open-source, academic, and commercial database replication systems and combine this material with case studies resulting from developing and deploying real systems at many customer sites .
Revised:  We sift through representative examples from the last decade of open-source, academic, and commercial database replication systems and combine this material with case studies resulting from developing and deploying real systems at many customer sites .
Edit intent: clarity
Original:  We sift through  the last decade of open-source, academic, and commercial database replication systems and combine this material with case studies resulting from developing and deploying real systems at many customer sites .
Revised:  We sift through the last decade of open-source, academic, and commercial database replication systems and combine this material with case studies from real systems deployed at Fortune 500 customers .
Edit intent: clarity
Original:  We propose two agendas, one for academic research and one for industrial R&D, which we expect can bridge the gaps within 5-10 years  .
Revised:  We propose two agendas, one for academic research and one for industrial R&D, which we believe can bridge the gaps within 5-10 years .
Edit intent: clarity
Original:  We propose two agendas, one for academic research and one for industrial R&D, which we expect can bridge the gaps within 5-10 years  .
Revised:  We propose two agendas, one for academic research and one for industrial R&D, which we expect can bridge the gap within 5-10 years .
Edit intent: fluency
Original:  Our model generically predicts striking cusps in the distribution of  fitness effects of fixed mutations and predicts that a single element of the chemotype should comprise all mutations at the high fitness end of that distribution . Using extreme value theory, we show that the most fit pair of these cusps are typically well-separated, even when the chemotype consists of thousands of elements , implying that the effects we predict should be observable in practical experiments .
Revised:  Our model generically predicts striking cusps in the distribution of the fitness effects of fixed mutations and predicts that a single element of the chemotype should comprise all mutations at the high fitness end of that distribution . Using extreme value theory, we show that the most fit pair of these cusps are typically well-separated, even when the chemotype consists of thousands of elements , implying that the effects we predict should be observable in practical experiments .
Edit intent: fluency
Original:  Our model generically predicts striking cusps in the distribution of  fitness effects of fixed mutations and predicts that a single element of the chemotype should comprise all mutations at the high fitness end of that distribution . Using extreme value theory, we show that the most fit pair of these cusps are typically well-separated, even when the chemotype consists of thousands of elements , implying that the effects we predict should be observable in practical experiments .
Revised:  Our model generically predicts striking cusps in the distribution of fitness effects of fixed mutations and predicts that a single element of the chemotype should comprise all mutations at the high-fitness ends of these distributions . Using extreme value theory, we show that the most fit pair of these cusps are typically well-separated, even when the chemotype consists of thousands of elements , implying that the effects we predict should be observable in practical experiments .
Edit intent: clarity