wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Previously, O(n\log n) time algorithms were known which are based on the technique for computing the minimum weight k-link path given in \mbox{%DIFAUXCMD kgon94,kgon95soda  By applying the new technique proposed in Jin's recent work for the dual problem of computing the maximum area triangle inside a convex polygon, we solve the problem at hand in O(n) time, thus justify Jin's claim that his technique may find applications in other polygonal inclusion problems.
Revised:  Previously, O(n\log n) time algorithms were known which are based on the technique for computing the minimum weight k-link path given in \mbox{%DIFAUXCMD kgon94,kgon95soda . By applying the new technique proposed in Jin's recent work for the dual problem of computing the maximum area triangle inside a convex polygon, we solve the problem at hand in O(n) time, thus justify Jin's claim that his technique may find applications in other polygonal inclusion problems.
Edit intent: fluency
Original:  Previously, O(n\log n) time algorithms were known which are based on the technique for computing the minimum weight k-link path given in \mbox{%DIFAUXCMD kgon94,kgon95soda  By applying the new technique proposed in Jin's recent work for the dual problem of computing the maximum area triangle inside a convex polygon, we solve the problem at hand in O(n) time, thus justify Jin's claim that his technique may find applications in other polygonal inclusion problems.
Revised:  Previously, O(n\log n) time algorithms were known which are based on the technique for computing the minimum weight k-link path given in \mbox{%DIFAUXCMD kgon94,kgon95soda By applying the new technique proposed in Jin's recent work for the dual problem of computing the maximum area triangle inside a convex polygon, we solve the problem at hand in O(n) time, thus justify Jin's claim that his technique may find applications in other polygon inclusion problems.
Edit intent: fluency
Original:  Previously, } O(n  \log n) time algorithms were known which are based on the technique for computing the minimum weight k-link path given in [A. Aggarwal et. al. DCG94;
Revised:  Building on the Rotate-and-Kill technique } O(n \log n) time algorithms were known which are based on the technique for computing the minimum weight k-link path given in [A. Aggarwal et. al. DCG94;
Edit intent: meaning-changed
Original:  Previously, } O(n  \log n) time algorithms were known which are based on the technique for computing the minimum weight k-link path given in [A. Aggarwal et. al. DCG94;
Revised:  Previously, Arxiv:1707.04071} O(n \log n) time algorithms were known which are based on the technique for computing the minimum weight k-link path given in [A. Aggarwal et. al. DCG94;
Edit intent: meaning-changed
Original:  Previously, } O(n  \log n) time algorithms were known which are based on the technique for computing the minimum weight k-link path given in [A. Aggarwal et. al. DCG94;
Revised:  Previously, }, we propose an algorithm that solves the problem in O(n \log n) time algorithms were known which are based on the technique for computing the minimum weight k-link path given in [A. Aggarwal et. al. DCG94;
Edit intent: meaning-changed
Original:  Previously, } O(n  \log n) time algorithms were known which are based on the technique for computing the minimum weight k-link path given in [A. Aggarwal et. al. DCG94;
Revised:  Previously, } O(n ) time, improving the best-known O(n \log n) time algorithms were known which are based on the technique for computing the minimum weight k-link path given in [A. Aggarwal et. al. DCG94;
Edit intent: meaning-changed
Original:  SODA95}. By applying the new technique proposed in Jin's recent work for the dual problem of computing the maximum area triangle inside a convex polygon, we solve the problem at hand in O(n) time, thus justify Jin's claim that his technique may find applications in other polygon inclusion problems. Our algorithm actually computes all the local minimal area circumscribing triangles touching edge-to-edge.
Revised:  SODA95}. Our algorithm computes all the local minimal area circumscribing triangles touching edge-to-edge.
Edit intent: coherence
Original:  (iii) The third algorithm, that has an approximation ratio of 27, guards all interior and boundary points of P in O(n^5) time  .
Revised:  (iii) The third algorithm, that has an approximation ratio of 27, guards all interior and boundary points of P in O(n^5) time . Further, these algorithms can be modified to obtain similar approximation ratios while using edge guards .
Edit intent: meaning-changed
Original:  First, we show that quadtrees as a space-division data structure can be made smooth and dynamic subject to %DIFDELCMD < {\em %%% split and%DIFDELCMD < {\em %%% merge operations on the quadtree cells.
Revised:  First, we show that quadtrees as a space-division data structure can be made smooth and dynamic subject to %DIFDELCMD < {\em %%% and%DIFDELCMD < {\em %%% merge operations on the quadtree cells.
Edit intent: clarity
Original:  First, we show that quadtrees as a space-division data structure can be made smooth and dynamic subject to %DIFDELCMD < {\em %%% split and%DIFDELCMD < {\em %%% merge operations on the quadtree cells.
Revised:  First, we show that quadtrees as a space-division data structure can be made smooth and dynamic subject to %DIFDELCMD < {\em %%% split %DIFDELCMD < {\em %%% merge operations on the quadtree cells.
Edit intent: coherence
Original:  First, we show that quadtrees as a space-division data structure can be made smooth and dynamic subject to %DIFDELCMD < {\em %%% split and%DIFDELCMD < {\em %%% merge operations on the quadtree cells.
Revised:  First, we show that quadtrees as a space-division data structure can be made smooth and dynamic subject to %DIFDELCMD < {\em %%% split and%DIFDELCMD < {\em %%% split and merge operations on the quadtree cells.
Edit intent: clarity
Original:  Second, we show that quadtrees used to store a set of points in R^d can be made smooth and dynamic subject to %DIFDELCMD < {\em %%% insertions and%DIFDELCMD < {\em %%% deletions of points.
Revised:  Second, we show that quadtrees used to store a set of points in R^d can be made smooth and dynamic subject to %DIFDELCMD < {\em %%% and%DIFDELCMD < {\em %%% deletions of points.
Edit intent: fluency
Original:  Second, we show that quadtrees used to store a set of points in R^d can be made smooth and dynamic subject to %DIFDELCMD < {\em %%% insertions and%DIFDELCMD < {\em %%% deletions of points.
Revised:  Second, we show that quadtrees used to store a set of points in R^d can be made smooth and dynamic subject to %DIFDELCMD < {\em %%% insertions %DIFDELCMD < {\em %%% deletions of points.
Edit intent: coherence
Original:  Second, we show that quadtrees used to store a set of points in R^d can be made smooth and dynamic subject to %DIFDELCMD < {\em %%% insertions and%DIFDELCMD < {\em %%% deletions of points.
Revised:  Second, we show that quadtrees used to store a set of points in R^d can be made smooth and dynamic subject to %DIFDELCMD < {\em %%% insertions and%DIFDELCMD < {\em %%% insertions and deletions of points.
Edit intent: clarity
Original:  The second version uses the first but must additionally deal with %DIFDELCMD < {\em %%% compression and%DIFDELCMD < {\em %%% alignment of quadtree components.
Revised:  The second version uses the first but must additionally deal with %DIFDELCMD < {\em %%% and%DIFDELCMD < {\em %%% alignment of quadtree components.
Edit intent: clarity
Original:  The second version uses the first but must additionally deal with %DIFDELCMD < {\em %%% compression and%DIFDELCMD < {\em %%% alignment of quadtree components.
Revised:  The second version uses the first but must additionally deal with %DIFDELCMD < {\em %%% compression %DIFDELCMD < {\em %%% alignment of quadtree components.
Edit intent: fluency
Original:  The second version uses the first but must additionally deal with %DIFDELCMD < {\em %%% compression and%DIFDELCMD < {\em %%% alignment of quadtree components.
Revised:  The second version uses the first but must additionally deal with %DIFDELCMD < {\em %%% compression and%DIFDELCMD < {\em %%% compression and alignment of quadtree components.
Edit intent: coherence
Original:  In both cases our updates take 2^{O(d\log d )} time, except for the point location part in the second version which has a lower bound of \Theta (\log n)---but if a pointer ( %DIFDELCMD < {\em %%% finger ) to the correct quadtree cell is given, the rest of the updates take worst-case constant time.
Revised:  In both cases our updates take 2^{O(d\log d )} time, except for the point location part in the second version which has a lower bound of \Theta (\log n)---but if a pointer ( %DIFDELCMD < {\em %%% finger ) to the correct quadtree cell is given, the rest of the updates take worst-case constant time.
Edit intent: fluency
Original:  We computed the amplitude-period co-variation of ten benchmark biomolecular oscillators as their parameters were individually varied around a nominal value, cataloguing instances where an increasein period is accompanied by an increase or decrease in amplitude as well as more complex co-variations.
Revised:  We computed the amplitude-period co-variation of eleven benchmark biomolecular oscillators as their parameters were individually varied around a nominal value, cataloguing instances where an increasein period is accompanied by an increase or decrease in amplitude as well as more complex co-variations.
Edit intent: meaning-changed
Original:  We computed the amplitude-period co-variation of ten benchmark biomolecular oscillators as their parameters were individually varied around a nominal value, cataloguing instances where an increasein period is accompanied by an increase or decrease in amplitude as well as more complex co-variations. To account for the amplitudes of the many biomolecular species that may be part of the oscillation circuit, we use a power norm-based amplitude metric, finding an increase of instances where an increase in period correlates with an increase in this amplitude metric .
Revised:  We computed the amplitude-period co-variation of ten benchmark biomolecular oscillators as their parameters were individually varied around a nominal value, classifying the various co-variation patterns such as a simultaneous increase/ decrease in period and amplitude. Next, we repeated the classification using a power norm-based amplitude metric, to account for the amplitudes of the many biomolecular species that may be part of the oscillation circuit, we use a power norm-based amplitude metric, finding an increase of instances where an increase in period correlates with an increase in this amplitude metric .
Edit intent: clarity
Original:  Finally, we calculate "scaling laws" of period-amplitude co-variation for a subset of these benchmark oscillators , finding that as period increases the amplitude increases or remains constant . These resultsshould help to understand the amplitude-period co-variation of oscillators in biomolecular as well as other contexts .
Revised:  Finally, we calculate "scaling laws" of period-amplitude co-variation for a subset of these benchmark oscillators , finding that as the approximated period increases, the upper bound of the amplitude increases, or reaches a constant value. Based on these results, we discuss the effect of different parameters on the type of period-amplitude co-variation as well as other contexts .
Edit intent: meaning-changed
Original:  We propose to work in the following procedure: Applying the theory of the monotone dynamical system, we first establish the existence and uniqueness of classical solutions to the recursive DPEs by a truncation argument in the finite state space.
Revised:  We propose to work in the following procedure: Applying the theory of monotone dynamical system, we first establish the existence and uniqueness of classical solutions to the recursive DPEs by a truncation argument in the finite state space.
Edit intent: fluency
Original:  Building upon results in the first stage, we construct a sequence of approximating risk sensitive control problems with finite state space and prove that the resulting smooth value functions will converge to the classical solution of the original system of DPEs.
Revised:  Building upon results in the first stage, we construct a sequence of approximating risk sensitive control problems with finite states and prove that the resulting smooth value functions will converge to the classical solution of the original system of DPEs.
Edit intent: clarity
Original:  Applying CyHMMs to two real-world health-tracking datasets -- of human menstrual cycle symptoms and physical activity tracking data -- yields important insights including which symptoms to expect at each point during the cycle.
Revised:  Applying CyHMMs to two real-world health-tracking datasets -- of menstrual cycle symptoms and physical activity tracking data -- yields important insights including which symptoms to expect at each point during the cycle.
Edit intent: clarity
Original:  We evaluate our approach using call records matched to lending outcomesin a middle income South American country . Individuals in the highest quartile of risk by our measure are 7.4 times more likely to default than those in the lowest quartile.
Revised:  We evaluate our approach using call records matched to lending outcomesin a middle income South American country , individuals in the highest quartile of risk by our measure are 7.4 times more likely to default than those in the lowest quartile.
Edit intent: fluency
Original:  Individuals in the highest quartile of risk by our measure are 7.4 times more likely to default than those in the lowest quartile. The method is predictive for both individuals with financial histories, and those without, who cannot be scored using traditional methods. We benchmark performance on our sample of individuals with (thin) financial histories : our method performs no worse than models using credit bureau information  .
Revised:  Individuals in the highest quartile of risk by our measure are 7.4 times more likely to default than those in the lowest quintile. On our sample of individuals with (thin) financial histories : our method performs no worse than models using credit bureau information .
Edit intent: clarity
Original:  This paper shows that behavioral signatures in mobile phone data predict loan default, using call records matched to loan outcomes . In a middle income South American country, individuals in the highest quintile of risk by our measure are 2.8 times more likely to default than those in the lowest quintile. On our sample of individuals with (thin) financial histories, our method  outperforms models using credit bureau information, both within time and when tested on a different time period.
Revised:  This paper shows that behavioral signatures in mobile phone data predict loan default, using call records matched to repayment outcomes for credit extended by a South American telecom. On a sample of individuals with (thin) financial histories, our method outperforms models using credit bureau information, both within time and when tested on a different time period.
Edit intent: clarity
Original:   The method forms the basis for new forms of lending that reach the unbanked.
Revised:  But our method also attains similar performance on those without financial histories, who cannot be scored using traditional methods. Individuals in the highest quintile of risk by our measure are 2.8 times more likely to default than those in the lowest quintile. The method forms the basis for new forms of lending that reach the unbanked.
Edit intent: meaning-changed
Original:  Using only two ranked tables  with microbes' nutrient preferences and  competitive abilities, we can determine all the stable states as well as the specific perturbations driving a community from one state to another. Using an example of 7 Bacteroides species utilizing 9 polysaccharides common to the human gut  , we predict that mutual complementarity in nutrient preferences enables these species to coexist at high abundances.
Revised:  Using only two ranked tables with microbes' nutrient preferences and competitive abilities, we can determine all the stable states as well as predict inter-state transitions, triggered by the removal or addition of a specific nutrient or microbe. Further, using an example of 7 Bacteroides species utilizing 9 polysaccharides common to the human gut , we predict that mutual complementarity in nutrient preferences enables these species to coexist at high abundances.
Edit intent: clarity
Original:  Using an example of 7 Bacteroides species utilizing 9 polysaccharides common to the human gut  , we predict that mutual complementarity in nutrient preferences enables these species to coexist at high abundances.
Revised:  Using an example of 7 Bacteroides species common to the human gut , we predict that mutual complementarity in nutrient preferences enables these species to coexist at high abundances.
Edit intent: clarity
Original:  Using an example of 7 Bacteroides species utilizing 9 polysaccharides common to the human gut  , we predict that mutual complementarity in nutrient preferences enables these species to coexist at high abundances.
Revised:  Using an example of 7 Bacteroides species utilizing 9 polysaccharides common to the human gut utilizing 9 polysaccharides , we predict that mutual complementarity in nutrient preferences enables these species to coexist at high abundances.
Edit intent: meaning-changed
Original:  We consider finite horizon optimal control to steer the network from an arbitrary initial state, defined in terms of active link set and supply-demand at  nodes, to a feasible state, i.e., a state that is invariant under the failure rule.
Revised:  We consider finite horizon optimal control to steer the network from an arbitrary initial state, defined in terms of active link set and supply-demand at the nodes, to a feasible state, i.e., a state that is invariant under the failure rule.
Edit intent: fluency
Original:  We consider finite horizon optimal control to steer the network from an arbitrary initial state, defined in terms of active link set and supply-demand at  nodes, to a feasible state, i.e., a state that is invariant under the failure rule.
Revised:  We consider finite horizon optimal control to steer the network from an arbitrary initial state, defined in terms of active link set and supply-demand at nodes, to a feasible state, i.e., a state which is invariant under the failure rule.
Edit intent: fluency
Original:  In the first iteration, optimal solutions to the local problems are computed, from leaf nodes to the root node, in terms of the coupling variables. In the second iteration, in the reverse order, the local optimal solutions are instantiated with specific values of the coupling variables. Restricted to constant controls, the optimal solutions to the local problems possess a piecewise linear property, which facilitates analytical solution.
Revised:  When restricted to the class of one-shot control actions, the optimal solutions to the local problems possess a piecewise linear property, which facilitates analytical solution.
Edit intent: clarity
Original:  We show that the Vietoris-Rips (resp. Cech) complex of a wedge sum, equipped with a natural metric, is homotopy equivalent to the wedge sum of the Vietoris-Rips (resp.
Revised:  We show that the Vietoris-Rips complex of a wedge sum, equipped with a natural metric, is homotopy equivalent to the wedge sum of the Vietoris-Rips (resp.
Edit intent: coherence
Original:  Cech) complex of a wedge sum, equipped with a natural metric, is homotopy equivalent to the wedge sum of the Vietoris-Rips (resp. Cech) complexes.
Revised:  Cech) complex of a wedge sum, equipped with a natural metric, is homotopy equivalent to the wedge sum of the Vietoris-Rips complexes.
Edit intent: clarity
Original:  As our main example, we deduce the homotopy type of the Vietoris-Rips complex of two metric graphs glued together along a sufficiently short path  .
Revised:  As our main example, we deduce the homotopy type of the Vietoris-Rips complex of two metric graphs glued together along a sufficiently short path (compared to lengths of certain loops in the input graphs) .
Edit intent: meaning-changed
Original: In the limited-workspace model , we assume that the input of size n lies in a random access read-only memory . The output has to be reported sequentially, and it cannot be accessed or modified .
Revised: In the limited-workspace model , we assume that S resides in a random-access memory that can only be read. The edges of the Euclidean minimum spanning tree \text{EMST to be reported sequentially, and it cannot be accessed or modified .
Edit intent: meaning-changed
Original:  The output has to be reported sequentially, and it cannot be accessed or modified . In addition, there is a read-write workspace of O(s ) words, where s \in \{1, \dots, n\} is a given parameter.
Revised:  The output has to be reported sequentially, and it cannot be accessed or modified afterwards. There is a parameter s \in \{1, \dots, n\} is a given parameter.
Edit intent: clarity
Original:  In addition, there is a read-write workspace of O(s ) words, where s \in \{1, \dots, n\} is a given parameter. In a time-space trade-off, we are interested in how the running time of an algorithm improves as s varies from 1 to n. We present a time-space trade-off for computing the Euclidean minimum spanning tree (EMST) of a set V of n sites in the plane. We present an algorithm that computes EMST(V) using O(S) in O}\big( (n^3 \log s /s^2) time and\big)  O(s) words of workspace.
Revised:  In addition, there is a read-write workspace of O(s ) words, where s \in \{1, \dots, n\} so that the algorithm may use O(s) cells of read-write memory (called the workspace) for its computations. Our goal is to find an algorithm that computes EMST(V) using O(S) in O}\big( (n^3 \log s /s^2) time and\big) O(s) words of workspace.
Edit intent: clarity
Original:  We present an algorithm that computes EMST(V) using O(S) in O}\big( (n^3 \log s /s^2) time and\big)  O(s) words of workspace.
Revised:  We present an algorithm that has the best possible running time for any given s between 1 and n. We show how to compute \text{EMST(S) in O}\big( (n^3 \log s /s^2) time and\big) O(s) words of workspace.
Edit intent: meaning-changed
Original:  We present an algorithm that computes EMST(V) using O(S) in O}\big( (n^3 \log s /s^2) time and\big)  O(s) words of workspace.
Revised:  We present an algorithm that computes EMST(V) using O(S) in O}\big( (n^3 /s^2) time and\big) O(s) words of workspace.
Edit intent: meaning-changed
Original:  We present an algorithm that computes EMST(V) using O(S) in O}\big( (n^3 \log s /s^2) time and\big)  O(s) words of workspace.
Revised:  We present an algorithm that computes EMST(V) using O(S) in O}\big( (n^3 \log s /s^2) \log s\big) O(s) words of workspace.
Edit intent: clarity
Original:  We present an algorithm that computes EMST(V) using O(S) in O}\big( (n^3 \log s /s^2) time and\big)  O(s) words of workspace.
Revised:  We present an algorithm that computes EMST(V) using O(S) in O}\big( (n^3 \log s /s^2) time and\big) time with O(s) words of workspace.
Edit intent: clarity
Original:  We present an algorithm that computes EMST(V) using O(S) in O}\big( (n^3 \log s /s^2) time and\big)  O(s) words of workspace. Our algorithm uses the fact that EMST(V) is a subgraph of the bounded-degree relative neighborhood graph of V, and applies(S) is exactly \text{EMST}(S).
Revised:  We present an algorithm that computes EMST(V) using O(S) in O}\big( (n^3 \log s /s^2) time and\big) O(s) cells of workspace, giving a smooth trade-off between the two best known bounds O(n^3) for s = 1 and O(n \log n) for s = n. For this, we run Kruskal's algorithm on the relative neighborhood graph (RNG) of S. It is a classic fact that the minimum spanning tree of \text{RNG(S) is exactly \text{EMST}(S).
Edit intent: meaning-changed