wanyu/IteraTeR_v2 huggingface dataset:
Original: Using a combination of theory and high-precision simulations, we study the translocation of a RNA molecule, pulled through a  nanopore by an optical tweezer, as a method to determine its secondary structure.
Revised: Using a combination of theory and high-precision simulations, we study the translocation of an RNA molecule, pulled through a nanopore by an optical tweezer, as a method to determine its secondary structure.
Edit intent: fluency
Original:  Risk-avoiding agents choose their fraction q(t) proportional to the expected positive RoI, while risk-seeking agents always choose a maximum value q_{max} if they predict the RoI to be positive ( `` everything on red '' ).
Revised:  Risk-avoiding agents choose their fraction q(t) proportional to the expected positive RoI, while risk-seeking agents always choose a maximum value q_{max} if they predict the RoI to be positive ( " everything on red '' ).
Edit intent: fluency
Original:  Risk-avoiding agents choose their fraction q(t) proportional to the expected positive RoI, while risk-seeking agents always choose a maximum value q_{max} if they predict the RoI to be positive ( `` everything on red '' ).
Revised:  Risk-avoiding agents choose their fraction q(t) proportional to the expected positive RoI, while risk-seeking agents always choose a maximum value q_{max} if they predict the RoI to be positive ( `` everything on red " ).
Edit intent: fluency
Original:  We develop a perturbative approach that utilizes the dominating movement of the network stationary states in the state space.
Revised:  We develop a perturbative approach that utilizes the dominant movement of the network stationary states in the state space.
Edit intent: fluency
Original:  In this work, we want to explore this paradoxand provide fundamental understanding on power control .
Revised:  In this work, we want to understand this paradox .
Edit intent: clarity
Original:  Specifically, we want to explore the following questions: (1)Theoretically, should we increase or decrease transmission power to maximize network capacity?
Revised:  Specifically, we address the following questions: (1)Theoretically, should we increase or decrease transmission power to maximize network capacity?
Edit intent: clarity
Original:  (2) Theoretically, how much network capacity gain can we achieve when using power control?
Revised:  (2) Theoretically, how much network capacity gain can we achieve by power control?
Edit intent: clarity
Original: We develop a theory of first passage processes in stochastic non-equilibrium systems of reaction kinetic (or birth-death ) type using a well known epidemiological SIR (Susceptible - Infected - Recovered) model as a prototypical example .
Revised: We develop a theory of first passage processes in stochastic non-equilibrium systems of birth-death ) type using a well known epidemiological SIR (Susceptible - Infected - Recovered) model as a prototypical example .
Edit intent: clarity
Original:  In this way the problem is reduced to finding an optimal path to extinction: a heteroclinic trajectory of an effective multi-dimensional classical Hamiltonian system.
Revised:  In this way the problem is reduced to finding the optimal path to extinction: a heteroclinic trajectory of an effective multi-dimensional classical Hamiltonian system.
Edit intent: fluency
Original:  We determine this trajectory and mean extinction time numerically in general case and analytically close to the bifurcation point.
Revised:  We compute this trajectory and mean extinction time numerically in general case and analytically close to the bifurcation point.
Edit intent: clarity
Original:  Its variant called "Maximum Compatible Tree" MCT is less stringent, as it allows the input trees to be refined.
Revised:  Its variant called "Maximum Compatible Tree" (MCT) is less stringent, as it allows the input trees to be refined.
Edit intent: fluency
Original:  As a counterpart, we show that the problem is W[1]-hard with respect to parameter D. Moreover, elying on recent advances in parameterized complexity we obtain a tight lower bound: while MAST can be solved in O(N^{O(D)}) time where N denotes the input length, we show that an O(N^{o(D)}) bound is not achievable, unless SNP is contained in SE.
Revised:  As a counterpart, we show that the problem is W[1]-hard with respect to parameter D. Moreover, relying on recent advances in parameterized complexity we obtain a tight lower bound: while MAST can be solved in O(N^{O(D)}) time where N denotes the input length, we show that an O(N^{o(D)}) bound is not achievable, unless SNP is contained in SE.
Edit intent: fluency
Original: Let PCP(k) denote the k-rule Post Correspondence Problem and let ACCESSIBILITY(k) denote the the accessibility problem for k-rule semi-Thue systems.
Revised: Let PCP(k) denote the Post Correspondence Problem and let ACCESSIBILITY(k) denote the the accessibility problem for k-rule semi-Thue systems.
Edit intent: fluency
Original: Let PCP(k) denote the k-rule Post Correspondence Problem and let ACCESSIBILITY(k) denote the the accessibility problem for k-rule semi-Thue systems.
Revised: Let PCP(k) denote the k-rule Post Correspondence Problem and let ACCESSIBILITY(k) denote the the word problem for k-rule semi-Thue systems.
Edit intent: clarity
Original:  These molecules distinction is followed by specific balanced atom number and/or nucleon number distinctions within those molecules.  ]
Revised:  These molecules distinction is followed by specific balanced atom number and/or nucleon number distinctions within those molecules. ].
Edit intent: fluency
Original: Untangling is a process in which some vertices of a plane graph are moved to obtain a straight-line plane drawing.
Revised: Untangling is a process in which some vertices of a planar graph are moved to obtain a straight-line plane drawing.
Edit intent: clarity
Original:  For any graph G, we also present an upper bound for the number of fixed vertices in the worst case.
Revised:  For any graph G, we also present an upper bound on the number of fixed vertices in the worst case.
Edit intent: fluency
Original:  The bound is a function of the number of vertices, maximum degree and diameter of G. One of its consequences is the upper bound O((n \log n)^{2/3}) for all 3-vertex-connected planar graphs.
Revised:  The bound is a function of the number of vertices, maximum degree and diameter of G. One of its consequences is the upper bound O((n log n)^{2/3}) for all 3-vertex-connected planar graphs.
Edit intent: clarity
Original: In this paper we prove that for any uniformly recurrent infinite word W  , the following conditions are equivalent: (I) all complete returns to palindromes are palindromes;
Revised: In this paper we prove that for any infinite word W , the following conditions are equivalent: (I) all complete returns to palindromes are palindromes;
Edit intent: clarity
Original: Despite being the most popular methods of data analysis, Fourier-based techniques suffer from the problem of static resolution which is currently believed to be a fundamental limitation of the Fourier Transform.
Revised: Despite being the most popular methods of data analysis, Fourier-based techniques suffer from the problem of static resolution that is currently believed to be a fundamental limitation of the Fourier Transform.
Edit intent: fluency
Original: In this paper we consider the problem of monitoring an art gallery modeled as a polygon, the edges of which are arcs of curves, with edge or mobile guards.
Revised: We consider the problem of monitoring an art gallery modeled as a polygon, the edges of which are arcs of curves, with edge or mobile guards.
Edit intent: clarity
Original:  We show that : (1) \lfloorn+1{3}\rfloor diagonal guards are always sufficient and sometimes necessary, and (2) \lfloor2n+1{5}\rfloor edge guards are always sufficient and %DIFDELCMD < \lfloor%%% \frac{2n{5}}%DIFDELCMD < \rfloor %%% edge guards are sometimes necessary, in order to 2-dominate a triangulation graph.
Revised:  We show that \lfloorn+1{3}\rfloor diagonal guards are always sufficient and sometimes necessary, and (2) \lfloor2n+1{5}\rfloor edge guards are always sufficient and %DIFDELCMD < \lfloor%%% \frac{2n{5}}%DIFDELCMD < \rfloor %%% edge guards are sometimes necessary, in order to 2-dominate a triangulation graph.
Edit intent: fluency
Original:  We show that : (1) \lfloorn+1{3}\rfloor diagonal guards are always sufficient and sometimes necessary, and (2) \lfloor2n+1{5}\rfloor edge guards are always sufficient and %DIFDELCMD < \lfloor%%% \frac{2n{5}}%DIFDELCMD < \rfloor %%% edge guards are sometimes necessary, in order to 2-dominate a triangulation graph.
Revised:  We show that : (1) \lfloorn+1{3}\rfloor diagonal guards or \lfloor2n+1{5}\rfloor edge guards are always sufficient and %DIFDELCMD < \lfloor%%% \frac{2n{5}}%DIFDELCMD < \rfloor %%% edge guards are sometimes necessary, in order to 2-dominate a triangulation graph.
Edit intent: clarity
Original:  We show that : (1) \lfloorn+1{3}\rfloor diagonal guards are always sufficient and sometimes necessary, and (2) \lfloor2n+1{5}\rfloor edge guards are always sufficient and %DIFDELCMD < \lfloor%%% \frac{2n{5}}%DIFDELCMD < \rfloor %%% edge guards are sometimes necessary, in order to 2-dominate a triangulation graph.
Revised:  We show that : (1) \lfloorn+1{3}\rfloor diagonal guards are always sufficient and sometimes necessary, and (2) \lfloor2n+1{5}\rfloor edge guards are always sufficient and %DIFDELCMD < \lfloor%%% \frac{2n{5}}%DIFDELCMD < \rfloor %%% sometimes necessary, in order to 2-dominate a triangulation graph.
Edit intent: fluency
Original:  \lfloor{3}}\rfloor \lfloor{5}}\rfloor \lfloor{7}}\rfloor  Based on the above-mentioned results, we prove that, for piecewise-convex polygons, we can compute: (1) a mobile guard set of size \lfloorn+1{3}\rfloor in O(nn) time, (2) an edge guard set of size \lfloor2n+1{5}\rfloor in O(n^2) time, and (3) an edge guard set of size \lfloor\frac{3n}{7}\rfloor in O(n\log{}n) time.
Revised:  \lfloor\frac{n+1{3}}\rfloor \lfloor{5}}\rfloor \lfloor{7}}\rfloor Based on the above-mentioned results, we prove that, for piecewise-convex polygons, we can compute: (1) a mobile guard set of size \lfloorn+1{3}\rfloor in O(nn) time, (2) an edge guard set of size \lfloor2n+1{5}\rfloor in O(n^2) time, and (3) an edge guard set of size \lfloor\frac{3n}{7}\rfloor in O(n\log{}n) time.
Edit intent: fluency
Original:  \lfloor{3}}\rfloor \lfloor{5}}\rfloor \lfloor{7}}\rfloor  Based on the above-mentioned results, we prove that, for piecewise-convex polygons, we can compute: (1) a mobile guard set of size \lfloorn+1{3}\rfloor in O(nn) time, (2) an edge guard set of size \lfloor2n+1{5}\rfloor in O(n^2) time, and (3) an edge guard set of size \lfloor\frac{3n}{7}\rfloor in O(n\log{}n) time.
Revised:  \lfloor{3}}\rfloor \lfloor\frac{2n+1{5}}\rfloor \lfloor{7}}\rfloor Based on the above-mentioned results, we prove that, for piecewise-convex polygons, we can compute: (1) a mobile guard set of size \lfloorn+1{3}\rfloor in O(nn) time, (2) an edge guard set of size \lfloor2n+1{5}\rfloor in O(n^2) time, and (3) an edge guard set of size \lfloor\frac{3n}{7}\rfloor in O(n\log{}n) time.
Edit intent: fluency
Original:  \lfloor{3}}\rfloor \lfloor{5}}\rfloor \lfloor{7}}\rfloor  Based on the above-mentioned results, we prove that, for piecewise-convex polygons, we can compute: (1) a mobile guard set of size \lfloorn+1{3}\rfloor in O(nn) time, (2) an edge guard set of size \lfloor2n+1{5}\rfloor in O(n^2) time, and (3) an edge guard set of size \lfloor\frac{3n}{7}\rfloor in O(n\log{}n) time.
Revised:  \lfloor{3}}\rfloor \lfloor{5}}\rfloor \lfloor\frac{3n{7}}\rfloor Based on the above-mentioned results, we prove that, for piecewise-convex polygons, we can compute: (1) a mobile guard set of size \lfloorn+1{3}\rfloor in O(nn) time, (2) an edge guard set of size \lfloor2n+1{5}\rfloor in O(n^2) time, and (3) an edge guard set of size \lfloor\frac{3n}{7}\rfloor in O(n\log{}n) time.
Edit intent: fluency
Original:  \lfloor{3}}\rfloor \lfloor{5}}\rfloor \lfloor{7}}\rfloor  Based on the above-mentioned results, we prove that, for piecewise-convex polygons, we can compute: (1) a mobile guard set of size \lfloorn+1{3}\rfloor in O(nn) time, (2) an edge guard set of size \lfloor2n+1{5}\rfloor in O(n^2) time, and (3) an edge guard set of size \lfloor\frac{3n}{7}\rfloor in O(n\log{}n) time.
Revised:  \lfloor{3}}\rfloor \lfloor{5}}\rfloor \lfloor{7}}\rfloor in O(n) time. Based on the above-mentioned results, we prove that, for piecewise-convex polygons, we can compute: (1) a mobile guard set of size \lfloorn+1{3}\rfloor in O(nn) time, (2) an edge guard set of size \lfloor2n+1{5}\rfloor in O(n^2) time, and (3) an edge guard set of size \lfloor\frac{3n}{7}\rfloor in O(n\log{}n) time.
Edit intent: fluency
Original:  \lfloor{3}}\rfloor \lfloor{5}}\rfloor \lfloor{7}}\rfloor  Based on the above-mentioned results, we prove that, for piecewise-convex polygons, we can compute: (1) a mobile guard set of size \lfloorn+1{3}\rfloor in O(nn) time, (2) an edge guard set of size \lfloor2n+1{5}\rfloor in O(n^2) time, and (3) an edge guard set of size \lfloor\frac{3n}{7}\rfloor in O(n\log{}n) time.
Revised:  \lfloor{3}}\rfloor \lfloor{5}}\rfloor \lfloor{7}}\rfloor Based on the above-mentioned results, we prove that, for piecewise-convex polygons, we can compute: a mobile guard set of size \lfloorn+1{3}\rfloor in O(nn) time, (2) an edge guard set of size \lfloor2n+1{5}\rfloor in O(n^2) time, and (3) an edge guard set of size \lfloor\frac{3n}{7}\rfloor in O(n\log{}n) time.
Edit intent: fluency
Original:  \lfloor{3}}\rfloor \lfloor{5}}\rfloor \lfloor{7}}\rfloor  Based on the above-mentioned results, we prove that, for piecewise-convex polygons, we can compute: (1) a mobile guard set of size \lfloorn+1{3}\rfloor in O(nn) time, (2) an edge guard set of size \lfloor2n+1{5}\rfloor in O(n^2) time, and (3) an edge guard set of size \lfloor\frac{3n}{7}\rfloor in O(n\log{}n) time.
Revised:  \lfloor{3}}\rfloor \lfloor{5}}\rfloor \lfloor{7}}\rfloor Based on the above-mentioned results, we prove that, for piecewise-convex polygons, we can compute: (1) a mobile guard set of size \lfloorn+1{3}\rfloor in O(nn) time, an edge guard set of size \lfloor2n+1{5}\rfloor in O(n^2) time, and (3) an edge guard set of size \lfloor\frac{3n}{7}\rfloor in O(n\log{}n) time.
Edit intent: fluency
Original:  \lfloor{3}}\rfloor \lfloor{5}}\rfloor \lfloor{7}}\rfloor  Based on the above-mentioned results, we prove that, for piecewise-convex polygons, we can compute: (1) a mobile guard set of size \lfloorn+1{3}\rfloor in O(nn) time, (2) an edge guard set of size \lfloor2n+1{5}\rfloor in O(n^2) time, and (3) an edge guard set of size \lfloor\frac{3n}{7}\rfloor in O(n\log{}n) time.
Revised:  \lfloor{3}}\rfloor \lfloor{5}}\rfloor \lfloor{7}}\rfloor Based on the above-mentioned results, we prove that, for piecewise-convex polygons, we can compute: (1) a mobile guard set of size \lfloorn+1{3}\rfloor in O(nn) time, (2) an edge guard set of size \lfloor2n+1{5}\rfloor in O(n^2) time, and an edge guard set of size \lfloor\frac{3n}{7}\rfloor in O(n\log{}n) time.
Edit intent: fluency
Original:  Finally, we show that \lfloor\frac{n}{3}\rfloor mobile or \lceil{3}}\rceil edge guards are sometimes necessary.
Revised:  Finally, we show that \lfloor\frac{n}{3}\rfloor mobile or \lceil\frac{n{3}}\rceil edge guards are sometimes necessary.
Edit intent: fluency
Original:  such an guard set\lceil{4}}\rceil can be computed in O(n) time and space .
Revised:  such an guard set\lceil{4}}\rceil, can be computed in O(n) time and space .
Edit intent: fluency
Original:  such an guard set\lceil{4}}\rceil can be computed in O(n) time and space .
Revised:  such an guard set\lceil{4}}\rceil can be computed in O(n) time .
Edit intent: clarity
Original:  It is shown that myopic actions can be obtained with a simple counting procedure without knowing the underlying Markovian model .
Revised:  It is shown that the myopic policy has a semi-universal structure that reduces channel selection to a simple round-robin procedure and obviates the need to know the underlying Markov transition probabilities .
Edit intent: clarity
Original:  The optimality of the myopic policy is proved for the case of two channels and conjectured based on simulations for the general case  .
Revised:  The optimality of the myopic policy is proved for the case of two channels and conjectured for the general case .
Edit intent: clarity
Original: Using a known relationship between Shannon's mutual information and Fisher information, we derive an analytical expression for the sigmoidal tuning curve that ensures maximum information about a stimulus is encoded by a noisy sensory neural system .
Revised: A general method for deriving maximally informative sigmoidal tuning curves for neural systems with small normalized variability is presented .
Edit intent: clarity
Original:  The derivation also provides a solution to the converse problem of optimizing the stimulus distribution for a given sigmoidal tuning curve.
Revised:  The derivation also provides a solution to the converse problem of optimizing the stimulus distribution for a given tuning curve.
Edit intent: clarity
Original:  Using rate-distortion theory we show that maximum mutual information corresponds to Fisher-optimality only if the stimulus is uniform .
Revised:  Using rate-distortion theory we show that maximum mutual information corresponds to constant Fisher information only if the stimulus is uniform .
Edit intent: clarity
Original: Using a double parabola approximation to a recently prosposed mean-field theory of RNA solution, the problem packaging of RNA genomes  inside spherical viruses is studied.
Revised: The problem of RNA genomes inside spherical viruses is studied.
Edit intent: clarity
Original: Using a double parabola approximation to a recently prosposed mean-field theory of RNA solution, the problem packaging of RNA genomes  inside spherical viruses is studied.
Revised: Using a double parabola approximation to a recently prosposed mean-field theory of RNA solution, the problem packaging of RNA genomes packaged inside spherical viruses is studied.
Edit intent: clarity
Original:  For stronger adsorption strength , RNA concentration peaks at some distance near the capsid.
Revised:  For stronger capsid attraction , RNA concentration peaks at some distance near the capsid.
Edit intent: clarity
Original:  The numerical profile describes relatively well the experimentally observed RNA concentration profile of various viruses.
Revised:  The numerical profiles describe reasonably well the experimentally observed RNA concentration profile of various viruses.
Edit intent: clarity
Original:  For instance, we demonstrate from the free energy investigation how aromatic residues contribute to amyloid formation in three different manners: i) high hydrophobicity, ii) pi-stacking interaction along the fibrillar axis, and iii) high volume.
Revised:  For instance, we demonstrate from the free energy investigation how aromatic residues contribute to amyloid formation in three different manners: i) high hydrophobicity, ii) \pi-stacking interaction along the fibrillar axis, and iii) high volume.
Edit intent: fluency
Original:  Although the self-assembly process is highly efficient, aggregates not in the fibrillar form would also occur and it is important to include these `disordered ' species when discussing the thermodynamic equilibrium behaviour of the system.
Revised:  Although the self-assembly process is highly efficient, aggregates not in the fibrillar form would also occur and it is important to include these disordered species when discussing the thermodynamic equilibrium behaviour of the system.
Edit intent: fluency
Original:  For instance , we demonstrate from the free energy investigation how aromatic residues contribute to amyloid formation in three different manners: i) high hydrophobicity, ii) \pi-stacking interaction along the fibrillar axis, and iii) high volume.
Revised:  For instance , we demonstrate how aromatic residues contribute to amyloid formation in three different manners: i) high hydrophobicity, ii) \pi-stacking interaction along the fibrillar axis, and iii) high volume.
Edit intent: clarity
Original:  By basing the amyloid formation analysis on free energy discussion, our work opens up the possibility of a more quantitative consideration of amyloid formation.
Revised:  We then analyze how the formalism developed allows us to gain insight on the kinetic process of fibril formation.
Edit intent: clarity
Original: Protein aggregation in the form of a fibril, or protein amyloid , has important biological and technological implications.
Revised: Protein aggregation in the form of amyloid fibrils has important biological and technological implications.
Edit intent: clarity
Original:  Although the self-assembly process is highly efficient, aggregates not in the fibrillar form would also occur and it is important to include these disordered species when discussing the thermodynamic equilibrium behaviour of the system.
Revised:  Although the self-assembly process is highly efficient, aggregates not in the fibrillar form would also occur and it is important to include these disordered species when discussing the thermodynamic equilibrium behavior of the system.
Edit intent: fluency
Original:  By investigating the entropic and energetic components of the various species, we gain an understanding of the many empirical observations concerning the various amyloid promoting factors and the structural commonality among amyloids formed by different proteins.
Revised:  Starting with a model on the respective free energy densities for these species, we gain an understanding of the many empirical observations concerning the various amyloid promoting factors and the structural commonality among amyloids formed by different proteins.
Edit intent: clarity
Original:  Starting with a model on the respective free energy densities for these species, we calculate their concentrations at thermal equilibrium.
Revised:  Starting with a model on the respective binding free energies for these species, we calculate their concentrations at thermal equilibrium.
Edit intent: clarity
Original: Well-centered meshes (meshes composed of well-centered simplices ) have the advantage of having nice orthogonal dual meshes (the dual Voronoi diagram) , which is useful for certain numerical algorithms that require or prefer such primal-dual mesh pairs.
Revised: Meshes composed of well-centered simplices ) have the advantage of having nice orthogonal dual meshes (the dual Voronoi diagram) , which is useful for certain numerical algorithms that require or prefer such primal-dual mesh pairs.
Edit intent: clarity
Original: Well-centered meshes (meshes composed of well-centered simplices ) have the advantage of having nice orthogonal dual meshes (the dual Voronoi diagram) , which is useful for certain numerical algorithms that require or prefer such primal-dual mesh pairs.
Revised: Well-centered meshes (meshes composed of well-centered simplices have nice orthogonal dual meshes (the dual Voronoi diagram) , which is useful for certain numerical algorithms that require or prefer such primal-dual mesh pairs.
Edit intent: coherence
Original: Well-centered meshes (meshes composed of well-centered simplices ) have the advantage of having nice orthogonal dual meshes (the dual Voronoi diagram) , which is useful for certain numerical algorithms that require or prefer such primal-dual mesh pairs.
Revised: Well-centered meshes (meshes composed of well-centered simplices ) have the advantage of having nice orthogonal dual meshes (the dual Voronoi diagram) . This is useful for certain numerical algorithms that require or prefer such primal-dual mesh pairs.
Edit intent: coherence
Original: Well-centered meshes (meshes composed of well-centered simplices ) have the advantage of having nice orthogonal dual meshes (the dual Voronoi diagram) , which is useful for certain numerical algorithms that require or prefer such primal-dual mesh pairs.
Revised: Well-centered meshes (meshes composed of well-centered simplices ) have the advantage of having nice orthogonal dual meshes (the dual Voronoi diagram) , which is useful for certain numerical algorithms that prefer such primal-dual mesh pairs.
Edit intent: clarity