wanyu/IteraTeR_full_sent huggingface dataset:
Original:  We prove that if C is a convex closed differentiable curve in the plane such that the convex hull of C contains the evolute of C, then the homotopy type of a Vietoris--Rips complex of a subset of n points from C can be computed in time O(n  \log n) . Furthermore, we show how to compute the k-dimensional persistent homology of these n points in running time O(n^2(k+\log n)), which is nearly quadratic in the number of vertices n . This improves upon the traditional persistent homology algorithm, which is cubic in the number of simplices of dimension at most k+1, and hence of running time O(n^{3(k+2)})
Revised:  We prove that if C is a convex closed differentiable curve in the plane such that the convex hull of C contains the evolute of C, then the homotopy type of a Vietoris--Rips complex of a subset of n points from C can be computed in time O(n \log n) ) algorithm for computing the k-dimensional persistent homology of these n points in running time O(n^2(k+\log n)), which is nearly quadratic in the number of vertices n . This improves upon the traditional persistent homology algorithm, which is cubic in the number of simplices of dimension at most k+1, and hence of running time O(n^{3(k+2)})
Edit intent: meaning-changed
Original:  Furthermore, we show how to compute the k-dimensional persistent homology of these n points in running time O(n^2(k+\log n)), which is nearly quadratic in the number of vertices n . This improves upon the traditional persistent homology algorithm, which is cubic in the number of simplices of dimension at most k+1, and hence of running time O(n^{3(k+2)})
Revised:  Furthermore, we show how to compute the k-dimensional persistent homology of a filtration of clique complexes of cyclic graphs on n vertices. This is nearly quadratic in the number of vertices n . This improves upon the traditional persistent homology algorithm, which is cubic in the number of simplices of dimension at most k+1, and hence of running time O(n^{3(k+2)})
Edit intent: meaning-changed
Original:  Furthermore, we show how to compute the k-dimensional persistent homology of these n points in running time O(n^2(k+\log n)), which is nearly quadratic in the number of vertices n . This improves upon the traditional persistent homology algorithm, which is cubic in the number of simplices of dimension at most k+1, and hence of running time O(n^{3(k+2)})
Revised:  Furthermore, we show how to compute the k-dimensional persistent homology of these n points in running time O(n^2(k+\log n)), which is nearly quadratic in the number of vertices n , and therefore a large improvement upon the traditional persistent homology algorithm, which is cubic in the number of simplices of dimension at most k+1, and hence of running time O(n^{3(k+2)})
Edit intent: clarity
Original:  in the number of vertices n  . We ask if there are other geometric settings in which computing persistent homology is (say) quadratic or cubic in the number of vertices, instead of in the number of simplices.
Revised:  in the number of vertices n . Our algorithm applies, for example, to Vietoris--Rips complexes of points sampled from a curve in \mathbb{R . We ask if there are other geometric settings in which computing persistent homology is (say) quadratic or cubic in the number of vertices, instead of in the number of simplices.
Edit intent: meaning-changed
Original: In mechanical models of DNA, twist-bend coupling is a cross interaction term originating from the asymmetry between major and minor grooves.
Revised: By combining analytical results and simulations of various coarse-grained models we investigate the minimal energy shape of DNA minicircles which are torsionally constrained by an imposed over or undertwist. We show that twist-bend coupling is a cross interaction term originating from the asymmetry between major and minor grooves.
Edit intent: meaning-changed
Original: In mechanical models of DNA, twist-bend coupling is a cross interaction term originating from the asymmetry between major and minor grooves. We show that such coupling induces minimal energy shapes of overtwisted DNA minicircles resembling rounded polygons, with a periodic alternance of parts with high and low curvature .
Revised: In mechanical models of DNA, twist-bend coupling is a cross interaction term discussed in the recent DNA literature, induces minimal energy shapes of overtwisted DNA minicircles resembling rounded polygons, with a periodic alternance of parts with high and low curvature .
Edit intent: meaning-changed
Original:  We show that such coupling induces minimal energy shapes of overtwisted DNA minicircles resembling rounded polygons, with a periodic alternance of parts with high and low curvature . The periodicity is close to that of the double helix and depends on the degree of overtwisting. From a simple elastic energy minimization ansatz we derive an analytical expression of the minicircle shape which matches very well the results obtained from simulations of various coarse-grained models of DNA. Finally, the calculation of the twist and bending energy of minicircles shows how these are governed by renormalized stiffness constants, not the bare ones.
Revised:  We show that such coupling induces minimal energy shapes of overtwisted DNA minicircles resembling rounded polygons, with a periodic alternance of parts with high and low curvature resembling rounded polygons. We briefly discuss the possible experimental relevance of these findings. We finally show that the twist and bending energy of minicircles shows how these are governed by renormalized stiffness constants, not the bare ones.
Edit intent: clarity
Original: Dominance by annual species is commonly viewed as a transient state in plant succession preceding eventual perennial dominance . However, circumstantial evidence suggests that annual-perennial interactions can cause priority effects, allowing persistent annual dominance when annuals are initially more common than perennials.
Revised: Dominance by annual plants has traditionally been considered a brief early stage of ecological succession preceding inevitable dominance by competitive perennials. A more recent, alternative view suggests that interactions between annuals and perennials can result in priority effects, allowing persistent annual dominance when annuals are initially more common than perennials.
Edit intent: clarity
Original:  However, circumstantial evidence suggests that annual-perennial interactions can cause priority effects, allowing persistent annual dominance when annuals are initially more common than perennials. The necessary conditions for these potential priority effects remain unknown despite the extensive effort devoted to restoration of native perennial dominance in systems invaded by exotic annuals.
Revised:  However, circumstantial evidence suggests that annual-perennial interactions can cause priority effects, allowing persistent annual dominance when annuals are initially more common . Such priority effects would complicate restoration of native perennial dominance in systems invaded by exotic annuals.
Edit intent: clarity
Original:   Using a simple simulation model, we show that long-term (500 years) priority effects in annual-perennial interactions are possible as long as the plants have low fecundity and show a competition-longevity tradeoffsuch that annuals are more competitive than perennial seedlings.
Revised:  However, the conditions under which these priority effects occur remain unknown. Using a simple simulation model, we show that long-term (500 years) priority effects in annual-perennial interactions are possible as long as the plants have low fecundity and show a competition-longevity tradeoffsuch that annuals are more competitive than perennial seedlings.
Edit intent: clarity
Original:   Using a simple simulation model, we show that long-term (500 years) priority effects in annual-perennial interactions are possible as long as the plants have low fecundity and show a competition-longevity tradeoffsuch that annuals are more competitive than perennial seedlings.
Revised:  Using a simple simulation model, we show that long-term (500 years) priority effects are possible as long as the plants have low fecundity and show a competition-longevity tradeoffsuch that annuals are more competitive than perennial seedlings.
Edit intent: clarity
Original:   Using a simple simulation model, we show that long-term (500 years) priority effects in annual-perennial interactions are possible as long as the plants have low fecundity and show a competition-longevity tradeoffsuch that annuals are more competitive than perennial seedlings.
Revised:  Using a simple simulation model, we show that long-term (500 years) priority effects in annual-perennial interactions are possible as long as the plants have low fecundity and show an establishment-longevity tradeoff, with annuals having competitive advantage over perennial seedlings.
Edit intent: clarity
Original: Dominance by annual plants has traditionally been considered a brief early stage of ecological succession preceding inevitable dominance by competitive perennials . A more recent, alternative view suggests that interactions between annuals and perennials can result in priority effects, causing annual dominance to persist  if they are initially more common.
Revised: Dominance by annual plants has traditionally been considered a brief early stage of ecological succession preceding inevitable dominance by competitive perennial plants . A more recent, alternative view suggests that interactions between annuals and perennials can result in priority effects, causing annual dominance to persist if they are initially more common.
Edit intent: fluency
Original: Dominance by annual plants has traditionally been considered a brief early stage of ecological succession preceding inevitable dominance by competitive perennials . A more recent, alternative view suggests that interactions between annuals and perennials can result in priority effects, causing annual dominance to persist  if they are initially more common.
Revised: Dominance by annual plants has traditionally been considered a brief early stage of ecological succession preceding inevitable dominance by competitive perennials . A more recent, alternative view suggests that interactions between annuals and perennials can result in priority effects, causing annual dominance to persist for decades if they are initially more common.
Edit intent: meaning-changed
Original:  Using a simple simulation model, we show that long-term ( 500 years ) priority effects are possible as long as the plants have low fecundity and show an establishment-longevity tradeoff, with annuals having competitive advantage over perennial seedlings.
Revised:  Using a simple simulation model, we show that long-term ( equilibrium ) priority effects are possible as long as the plants have low fecundity and show an establishment-longevity tradeoff, with annuals having competitive advantage over perennial seedlings.
Edit intent: meaning-changed
Original:  Using a simple simulation model, we show that long-term ( 500 years ) priority effects are possible as long as the plants have low fecundity and show an establishment-longevity tradeoff, with annuals having competitive advantage over perennial seedlings.
Revised:  Using a simple simulation model, we show that long-term ( 500 years ) priority effects are possible only when the plants have low fecundity and show an establishment-longevity tradeoff, with annuals having competitive advantage over perennial seedlings.
Edit intent: clarity
Original:  We also show that short-term (up to 50 years ) priority effects arise solely due to low fitness difference in cases where perennials dominate in the long term. These results provide a theoretical basis for predicting when restoration of annual-invaded grasslands requires active removal of annuals and timely reintroduction of perennials.
Revised:  We also show that short-term (up to 50 years ) priority effects are more likely and does not require the tradeoff. Our results provide a theoretical basis for predicting when restoration of annual-invaded grasslands requires active removal of annuals and timely reintroduction of perennials.
Edit intent: meaning-changed
Original: Dominance by annual plants has traditionally been considered a brief early stage of ecological succession preceding inevitable dominance by competitive perennial plants. A more recent, alternative view suggests that interactions between annuals and perennials can result in priority effects, causing annual dominance to persist for decades if they are initially more common. Such priority effectswould complicate restoration of native perennial grasslands that have been invaded by exotic annuals. However , the conditions under which these priority effects occur remain unknown.
Revised: 1. In many grassland communities, the identity of dominant species may be determined by initial frequency owing to priority effects. Yet , the conditions under which these priority effects occur remain unknown.
Edit intent: clarity
Original:  However , the conditions under which these priority effects occur remain unknown. Using a simple simulation model , we show that long-term (equilibrium ) priority effects are possible only when the plants have low fecundity and show an establishment-longevity tradeoff, with annuals having competitive advantage over perennial seedlings .
Revised:  However , the conditions under which these priority effects remain unclear. 2. Focusing on interactions between annual and perennial plants, we used a simulation model to investigate how longevity, fecundity, and the competitive ability of seedlings might affect the probability of equilibrium priority effects (alternative stable states) and transient priority effects (alternative transient states). 3. The model suggests that establishment-longevity tradeoff, with annuals having competitive advantage over perennial seedlings .
Edit intent: clarity
Original:  Using a simple simulation model , we show that long-term (equilibrium ) priority effects are possible only when the plants have low fecundity and show an establishment-longevity tradeoff, with annuals having competitive advantage over perennial seedlings .
Revised:  Using a simple simulation model , we show that long-term (equilibrium ) priority effects are possible only when the plants have low fecundity and show an establishment-longevity tradeoff, in which annuals have competitive advantage over perennial seedlings .
Edit intent: coherence
Original:  Using a simple simulation model , we show that long-term (equilibrium ) priority effects are possible only when the plants have low fecundity and show an establishment-longevity tradeoff, with annuals having competitive advantage over perennial seedlings . However, transient (but long-lasting over decades) priority effects are more likely and does not require the tradeoff. Our results provide a theoretical basis for predicting when restoration of annual-invaded grasslands requires active removal of annuals and timely reintroduction of perennials .
Revised:  Using a simple simulation model , we show that long-term (equilibrium ) priority effects are possible only when the plants have low fecundity and show an establishment-longevity tradeoff, with annuals having competitive advantage over perennial seedlings , is a necessary condition for equilibrium priority effects. Equilibrium priority effects also require low fecundity in both annuals and perennials and small fitness differences, as determined by their relative fecundity, survival probability, and competitive ability at the seedling stage. 4. Transient priority effects need only small fitness differences. Furthermore, the model indicate that transient priority effects could last several decades under a range of the parameter space, exceeding the duration of typical experiments and observations. 5. Synthesis: Our results suggest that equilibrium priority effects driven by a life-history trade-off are possible but may be uncommon because they require unrealistically low fecundity. In contrast, transient priority effects should be more likely. Previous empirical findings of priority effects in grasslands may mostly indicate alternative transient, rather than stable, states, or other mechanisms than a life-history tradeoff .
Edit intent: meaning-changed
Original: 1. In many grassland communities, the identity of dominant speciesmay be determined by initial frequency owing to priority effects. Yet, the conditions for these priority effects remain unclear. 2. Focusing on interactions between annual and perennial plants, we used a simulation model to investigate how longevity, fecundity, and the competitive ability of seedlings might affect the probability of equilibrium priority effects (alternative stable states) and transient priority effects (alternative transient states).
Revised: Life-history tradeoffs among species are major drivers of community assembly. Most studies investigate how tradeoffs promote deterministic coexistence of species. It remains unclear how tradeoffs may instead promote historically contingent exclusion of species, where species dominance is affected by initial abundances, causing alternative community states. Focusing on the establishment-longevity tradeoff, we study the transient dynamics and equilibrium outcomes of competitive interactions in a simulation model to investigate how longevity, fecundity, and the competitive ability of seedlings might affect the probability of equilibrium priority effects (alternative stable states) and transient priority effects (alternative transient states).
Edit intent: clarity
Original:  2. Focusing on interactions between annual and perennial plants, we used a simulation model to investigate how longevity, fecundity, and the competitive ability of seedlings might affect the probability of equilibrium priority effects (alternative stable states) and transient priority effects (alternative transient states). 3. The model suggests that establishment-longevity tradeoff, in which annuals have competitive advantage over perennial seedlings, is a necessary condition for equilibrium priority effects.
Revised:  2. Focusing on interactions between annual and perennial plants, we used a simulation model of plant community assembly. We show that, in this model, the establishment-longevity tradeoff, in which annuals have competitive advantage over perennial seedlings, is a necessary condition for equilibrium priority effects.
Edit intent: clarity
Original:  3. The model suggests that establishment-longevity tradeoff, in which annuals have competitive advantage over perennial seedlings, is a necessary condition for equilibrium priority effects. Equilibrium priority effects also require low fecundity in both annuals and perennials and small fitness differences, as determined by their relative fecundity, survival probability, and competitive ability at the seedling stage.
Revised:  3. The model suggests that establishment-longevity tradeoff, in which annuals have competitive advantage over perennial seedlings, is a necessary but not sufficient condition for alternative stable equilibria that require also low fecundity for both species. An analytical approximation of our simulation model demonstrates that alternative stable equilibria are driven by demographic stochasticity in the number of seeds arriving at each establishment site. This site-scale stochasticity is only affected by fecundity in both annuals and perennials and small fitness differences, as determined by their relative fecundity, survival probability, and competitive ability at the seedling stage.
Edit intent: meaning-changed
Original:  Equilibrium priority effects also require low fecundity in both annuals and perennials and small fitness differences, as determined by their relative fecundity, survival probability, and competitive ability at the seedling stage. 4. Transient priority effects need only small fitness differences. Furthermore, the model indicate that transient priority effects could last several decades under a range of the parameter space, exceeding the duration of typical experiments and observations. 5. Synthesis: Our results suggest that equilibrium priority effects driven by a life-history trade-off are possible but may be uncommon because they require unrealistically low fecundity . In contrast, transient priority effects should be more likely. Previous empirical findings of priority effects in grasslands may mostly indicate alternative transient , rather than stable , states, or other mechanisms than a life-history tradeoff .
Revised:  Equilibrium priority effects also require low fecundity and therefore occurs even in infinitely large communities. In many cases where the establishment-longevity tradeoff does not cause alternative stable equilibria, it still decreases the rate of convergence toward the single equilibrium, resulting in decades of transient dynamics that can appear indistinguishable from alternative stable equilibria in empirical studies .
Edit intent: coherence
Original:  But the statistical limitations of these models, which can have millions of parameters and are fit to MSAs of only hundreds or thousands of effective sequences using a procedure known as inverse Ising inference, are incompletely understood.
Revised:  But the statistical limitations of these models, which can have millions of parameters and are fit to MSAs of only thousands or hundreds of effective sequences using a procedure known as inverse Ising inference, are incompletely understood.
Edit intent: fluency
Original:  In this work we predict how model quality degrades as a function of the number of sequences N, sequence length L, amino-acid alphabet size q, and the degree of conservation of the MSA  in different applications of the Potts models: In "fitness" predictions of individual protein sequences,  predictions of the effects of single-point and multiple mutations, and 3-d contact prediction in protein structure.
Revised:  In this work we predict how model quality degrades as a function of the number of sequences N, sequence length L, amino-acid alphabet size q, and the degree of conservation of the MSA , in different applications of the Potts models: In "fitness" predictions of individual protein sequences, predictions of the effects of single-point and multiple mutations, and 3-d contact prediction in protein structure.
Edit intent: fluency
Original:  In this work we predict how model quality degrades as a function of the number of sequences N, sequence length L, amino-acid alphabet size q, and the degree of conservation of the MSA  in different applications of the Potts models: In "fitness" predictions of individual protein sequences,  predictions of the effects of single-point and multiple mutations, and 3-d contact prediction in protein structure.
Revised:  In this work we predict how model quality degrades as a function of the number of sequences N, sequence length L, amino-acid alphabet size q, and the degree of conservation of the MSA in different applications of the Potts models: In "fitness" predictions of individual protein sequences, in predictions of the effects of single-point and multiple mutations, and 3-d contact prediction in protein structure.
Edit intent: fluency
Original:  In this work we predict how model quality degrades as a function of the number of sequences N, sequence length L, amino-acid alphabet size q, and the degree of conservation of the MSA  in different applications of the Potts models: In "fitness" predictions of individual protein sequences,  predictions of the effects of single-point and multiple mutations, and 3-d contact prediction in protein structure.
Revised:  In this work we predict how model quality degrades as a function of the number of sequences N, sequence length L, amino-acid alphabet size q, and the degree of conservation of the MSA in different applications of the Potts models: In "fitness" predictions of individual protein sequences, predictions of the effects of single-point mutations, in "double mutant cycle" predictions of epistasis, and in 3-d contact prediction in protein structure.
Edit intent: meaning-changed