wanyu/IteraTeR_full_sent huggingface dataset:
Original:  First, we consider a unidirectional problem where a resource can only be allocated to a user located to its leftas exemplified here. Imagine a one-way city street with traffic flowing from right to left; a ride-sharing company has distributed its vehicles along the street, which are ready to pick up users waiting at various locations. Users equipped with smartphone ride-hailing apps can register their requests on a ride allocation system. The latter then attempts to service each user by assigning a vehicle with spare capacity located to the user's right such that the average "pick up" distance is minimized.
Revised:  First, we consider unidirectional assignment policies that allocate resources only to users located to their left.
Edit intent: clarity
Original:  We propose the Move to Right (MTR) policy which assigns the nearest available resource located to the right , and contrast it with the Unidirectional Gale-Shapley (UGS) Matching policyknown in the literature .
Revised:  We propose the Move to Right (MTR) policy , which scans from left to right assigning nearest rightmost available resource to a user , and contrast it with the Unidirectional Gale-Shapley (UGS) Matching policyknown in the literature .
Edit intent: meaning-changed
Original:  We propose the Move to Right (MTR) policy which assigns the nearest available resource located to the right , and contrast it with the Unidirectional Gale-Shapley (UGS) Matching policyknown in the literature .
Revised:  We propose the Move to Right (MTR) policy which assigns the nearest available resource located to the right , and contrast it to the Unidirectional Gale-Shapley (UGS) Matching policyknown in the literature .
Edit intent: fluency
Original:  We propose the Move to Right (MTR) policy which assigns the nearest available resource located to the right , and contrast it with the Unidirectional Gale-Shapley (UGS) Matching policyknown in the literature .
Revised:  We propose the Move to Right (MTR) policy which assigns the nearest available resource located to the right , and contrast it with the Unidirectional Gale-Shapley (UGS) matching policy .
Edit intent: clarity
Original:  While both these policies are optimal  , we show that they are equivalent with respect to the expected distance traveled by a request (request distance), although MTR tends to be fairer, i. e., has low variance.
Revised:  While both these policies are optimal among all unidirectional policies , we show that they are equivalent with respect to the expected distance traveled by a request (request distance), although MTR tends to be fairer, i. e., has low variance.
Edit intent: meaning-changed
Original:  Moreover, we show that when the locations of users and resources are modeled by statistical point processes,  the spatial system under unidirectional policies can be mapped to a temporal queuing system , thus allowing the application of a plethora of queuing theory results that yield closed form expressions.
Revised:  Moreover, we show that when user and resource locations are modeled by statistical point processes, the spatial system under unidirectional policies can be mapped to a temporal queuing system , thus allowing the application of a plethora of queuing theory results that yield closed form expressions.
Edit intent: clarity
Original:  Moreover, we show that when the locations of users and resources are modeled by statistical point processes,  the spatial system under unidirectional policies can be mapped to a temporal queuing system , thus allowing the application of a plethora of queuing theory results that yield closed form expressions.
Revised:  Moreover, we show that when the locations of users and resources are modeled by statistical point processes, and resources are allowed to satisfy more than one user, the spatial system under unidirectional policies can be mapped to a temporal queuing system , thus allowing the application of a plethora of queuing theory results that yield closed form expressions.
Edit intent: meaning-changed
Original:  Moreover, we show that when the locations of users and resources are modeled by statistical point processes,  the spatial system under unidirectional policies can be mapped to a temporal queuing system , thus allowing the application of a plethora of queuing theory results that yield closed form expressions.
Revised:  Moreover, we show that when the locations of users and resources are modeled by statistical point processes, the spatial system under unidirectional policies can be mapped into bulk service queuing systems , thus allowing the application of a plethora of queuing theory results that yield closed form expressions.
Edit intent: meaning-changed
Original:   We also consider the bidirectional problem where there are no directional restrictions on resource allocation and give an optimal policy that has lower expected time complexity than known algorithms in literature in resource rich regimes .
Revised:  As we consider a case where different resources can satisfy different numbers of users, we also generate new results for bulk service queues. We also consider the bidirectional problem where there are no directional restrictions on resource allocation and give an optimal policy that has lower expected time complexity than known algorithms in literature in resource rich regimes .
Edit intent: meaning-changed
Original:  The scaling, introduced by Iglehart (1969) to the actuarial literature, amounts to multiplying the Poisson rate \lambda \la by n, dividing the claim severity by \sqrt{n , and adjusting the premium rate so that net premium income remains constant.
Revised:  The scaling, introduced by Iglehart \mbox{%DIFAUXCMD I1969 to the actuarial literature, amounts to multiplying the Poisson rate \lambda \la by n, dividing the claim severity by \sqrt{n , and adjusting the premium rate so that net premium income remains constant.
Edit intent: meaning-changed
Original:  The scaling, introduced by Iglehart (1969) to the actuarial literature, amounts to multiplying the Poisson rate \lambda \la by n, dividing the claim severity by \sqrt{n , and adjusting the premium rate so that net premium income remains constant.
Revised:  The scaling, introduced by Iglehart (1969) to the actuarial literature, amounts to multiplying the Poisson rate \la by n, dividing the claim severity by \sqrt{n , and adjusting the premium rate so that net premium income remains constant.
Edit intent: clarity
Original:  The scaling, introduced by Iglehart (1969) to the actuarial literature, amounts to multiplying the Poisson rate \lambda \la by n, dividing the claim severity by \sqrt{n , and adjusting the premium rate so that net premium income remains constant.
Revised:  The scaling, introduced by Iglehart (1969) to the actuarial literature, amounts to multiplying the Poisson rate \lambda \la by n, dividing the claim severity by \sqrtn , and adjusting the premium rate so that net premium income remains constant.
Edit intent: fluency
Original:   Therefore, we think of the associated diffusion approximation as being `` asymptotic for large values of \lambda.'' \la We are the first to use a comparison method to prove convergence of the probability of ruin for the scaled CL process and to derive the rate of convergence.
Revised:  \% Therefore, we think of the associated diffusion approximation as being `` asymptotic for large values of \lambda.'' \la We are the first to use a comparison method to prove convergence of the probability of ruin for the scaled CL process and to derive the rate of convergence.
Edit intent: fluency
Original:   Therefore, we think of the associated diffusion approximation as being `` asymptotic for large values of \lambda.'' \la We are the first to use a comparison method to prove convergence of the probability of ruin for the scaled CL process and to derive the rate of convergence.
Revised:  Therefore, we think of the associated diffusion approximation as being " asymptotic for large values of \lambda.'' \la We are the first to use a comparison method to prove convergence of the probability of ruin for the scaled CL process and to derive the rate of convergence.
Edit intent: fluency
Original:   Therefore, we think of the associated diffusion approximation as being `` asymptotic for large values of \lambda.'' \la We are the first to use a comparison method to prove convergence of the probability of ruin for the scaled CL process and to derive the rate of convergence.
Revised:  Therefore, we think of the associated diffusion approximation as being `` asymptotic for large values of \la We are the first to use a comparison method to prove convergence of the probability of ruin for the scaled CL process and to derive the rate of convergence.
Edit intent: coherence
Original:   Therefore, we think of the associated diffusion approximation as being `` asymptotic for large values of \lambda.'' \la We are the first to use a comparison method to prove convergence of the probability of ruin for the scaled CL process and to derive the rate of convergence.
Revised:  Therefore, we think of the associated diffusion approximation as being `` asymptotic for large values of \lambda.'' \la." We are the first to use a comparison method to prove convergence of the probability of ruin for the scaled CL process and to derive the rate of convergence.
Edit intent: fluency
Original:  Moreover, we show that the rate of convergence for the ruin probability is of order O(n^{-1/2 \mO\big(}\big) , and we show that the convergence is {\it uniform} with respect to the surplus.
Revised:  Moreover, we show that the rate of convergence for the ruin probability is of order \mO\big(}\big) , and we show that the convergence is {\it uniform} with respect to the surplus.
Edit intent: meaning-changed
Original:  Moreover, we show that the rate of convergence for the ruin probability is of order O(n^{-1/2 \mO\big(}\big) , and we show that the convergence is {\it uniform} with respect to the surplus.
Revised:  Moreover, we show that the rate of convergence for the ruin probability is of order O(n^{-1/2 \mO\big(n^{-1/2}\big) , and we show that the convergence is {\it uniform} with respect to the surplus.
Edit intent: fluency
Original:  For the case of exponentially-distributed claims, we are able to improve the approximation arising from the diffusion, attaining a uniform O(n \mO\big( ^{ -1 } ) \big) rate of convergence \N . We also include two examples that illustrate our results.
Revised:  For the case of exponentially-distributed claims, we are able to improve the approximation arising from the diffusion, attaining a uniform \mO\big( ^{ -1 } ) \big) rate of convergence \N . We also include two examples that illustrate our results.
Edit intent: clarity
Original:  For the case of exponentially-distributed claims, we are able to improve the approximation arising from the diffusion, attaining a uniform O(n \mO\big( ^{ -1 } ) \big) rate of convergence \N . We also include two examples that illustrate our results.
Revised:  For the case of exponentially-distributed claims, we are able to improve the approximation arising from the diffusion, attaining a uniform O(n \mO\big(n ^{ -1 } ) \big) rate of convergence \N . We also include two examples that illustrate our results.
Edit intent: fluency
Original:  For the case of exponentially-distributed claims, we are able to improve the approximation arising from the diffusion, attaining a uniform O(n \mO\big( ^{ -1 } ) \big) rate of convergence \N . We also include two examples that illustrate our results.
Revised:  For the case of exponentially-distributed claims, we are able to improve the approximation arising from the diffusion, attaining a uniform O(n \mO\big( ^{ -k/2 } ) \big) rate of convergence \N . We also include two examples that illustrate our results.
Edit intent: meaning-changed
Original:  For the case of exponentially-distributed claims, we are able to improve the approximation arising from the diffusion, attaining a uniform O(n \mO\big( ^{ -1 } ) \big) rate of convergence \N . We also include two examples that illustrate our results.
Revised:  For the case of exponentially-distributed claims, we are able to improve the approximation arising from the diffusion, attaining a uniform O(n \mO\big( ^{ -1 } \big) rate of convergence \N . We also include two examples that illustrate our results.
Edit intent: fluency
Original:  For the case of exponentially-distributed claims, we are able to improve the approximation arising from the diffusion, attaining a uniform O(n \mO\big( ^{ -1 } ) \big) rate of convergence \N . We also include two examples that illustrate our results.
Revised:  For the case of exponentially-distributed claims, we are able to improve the approximation arising from the diffusion, attaining a uniform O(n \mO\big( ^{ -1 } ) \big) rate of convergence for arbitrary k \in\N . We also include two examples that illustrate our results.
Edit intent: meaning-changed
Original:  We propose a new interaction index called Shapley-Taylor interaction index . It decomposes the value of the game into terms that model the interactions between subsets of players, analogous to how the Taylor series represents a function in terms of its derivatives of various orders .
Revised:  We propose a new interaction index called Shapley-Taylor index that attributes the model's prediction to interactions of subsets of features up to some size k. The method is analogous to how the Taylor series represents a function in terms of its derivatives of various orders .
Edit intent: clarity
Original:  It decomposes the value of the game into terms that model the interactions between subsets of players, analogous to how the Taylor series represents a function in terms of its derivatives of various orders .
Revised:  It decomposes the value of the game into terms that model the interactions between subsets of players, analogous to how the truncated Taylor Series decomposes the function value at a certain point using its derivatives at a different point. In fact, we show that the Shapley Taylor index is equal to the Taylor Series of the multilinear extension of the set-theoretic behavior of the model .
Edit intent: meaning-changed
Original:  We contrast the Shapley-Taylor interaction index against the previously pro-posed Shapley Interaction index and the Banzhaf interaction index (cf. [ 2 ])  .
Revised:  We contrast the Shapley-Taylor interaction index against the previously pro-posed Shapley Interaction index and the Banzhaf interaction index (cf. [ 2 ]) from the cooperative game theory literature. We also apply the Shapley Taylor index to three models and identify interesting qualitative insights .
Edit intent: meaning-changed
Original:  Our online sketching algorithm can compress an N-element dataset to a sketch of size O(N^b \log ^3{N ) in O(N^{  b+1  } \log ^3{N ) time, where b < 1 when the query satisfies a data-dependent near-neighbor stability condition .
Revised:  Our online sketching algorithm compresses an N element dataset to a sketch of size O(N^b \log ^3{N ) in O(N^{ b+1 } \log ^3{N ) time, where b < 1 when the query satisfies a data-dependent near-neighbor stability condition .
Edit intent: clarity
Original:  Our online sketching algorithm can compress an N-element dataset to a sketch of size O(N^b \log ^3{N ) in O(N^{  b+1  } \log ^3{N ) time, where b < 1 when the query satisfies a data-dependent near-neighbor stability condition .
Revised:  Our online sketching algorithm can compress an N-element dataset to a sketch of size O(N^b \log ^3 N ) in O(N^{ b+1 } \log ^3{N ) time, where b < 1 when the query satisfies a data-dependent near-neighbor stability condition .
Edit intent: fluency
Original:  Our online sketching algorithm can compress an N-element dataset to a sketch of size O(N^b \log ^3{N ) in O(N^{  b+1  } \log ^3{N ) time, where b < 1 when the query satisfies a data-dependent near-neighbor stability condition .
Revised:  Our online sketching algorithm can compress an N-element dataset to a sketch of size O(N^b \log ^3{N ) in O(N^{ ( b+1 } \log ^3{N ) time, where b < 1 when the query satisfies a data-dependent near-neighbor stability condition .
Edit intent: fluency
Original:  Our online sketching algorithm can compress an N-element dataset to a sketch of size O(N^b \log ^3{N ) in O(N^{  b+1  } \log ^3{N ) time, where b < 1 when the query satisfies a data-dependent near-neighbor stability condition .
Revised:  Our online sketching algorithm can compress an N-element dataset to a sketch of size O(N^b \log ^3{N ) in O(N^{ b+1 ) } \log ^3{N ) time, where b < 1 when the query satisfies a data-dependent near-neighbor stability condition .
Edit intent: fluency
Original:  Our online sketching algorithm can compress an N-element dataset to a sketch of size O(N^b \log ^3{N ) in O(N^{  b+1  } \log ^3{N ) time, where b < 1 when the query satisfies a data-dependent near-neighbor stability condition .
Revised:  Our online sketching algorithm can compress an N-element dataset to a sketch of size O(N^b \log ^3{N ) in O(N^{ b+1 } \log ^3 N ) time, where b < 1 when the query satisfies a data-dependent near-neighbor stability condition .
Edit intent: fluency
Original:  Our online sketching algorithm can compress an N-element dataset to a sketch of size O(N^b \log ^3{N ) in O(N^{  b+1  } \log ^3{N ) time, where b < 1 when the query satisfies a data-dependent near-neighbor stability condition .
Revised:  Our online sketching algorithm can compress an N-element dataset to a sketch of size O(N^b \log ^3{N ) in O(N^{ b+1 } \log ^3{N ) time, where b < 1. This sketch can correctly report the nearest neighbors of any query that satisfies a stability condition parameterized by b .
Edit intent: clarity
Original:  Our  results shed new light on the memory-accuracy tradeoff for near-neighbor search. The techniques presented reveal a deep connection between the fundamental compressed sensing (or heavy hitters) recovery problem and near-neighbor search, leading to new insight for geometric search problems and implications for sketching algorithms .
Revised:  Our results shed new light on the memory-accuracy tradeoff for nearest neighbor search, and our sketch, which consists entirely of short integer arrays, has a variety of attractive features in practice. We evaluate the memory-recall tradeoff of our method on a friend recommendation task in the Google Plus social media network. We obtain orders of magnitude better compression than the random projection based alternative while retaining the ability to report the nearest neighbors of practical queries .
Edit intent: meaning-changed
Original:  The most success to date has come from finding methods for turning persistence diagrams into vectors in \mathbb{R in a way which preserves as much of the space of persistence diagrams as possible, commonly referred to as featurization.
Revised:  The most success to date has come from methods that map persistence diagrams into vectors in \mathbb{R in a way which preserves as much of the space of persistence diagrams as possible, commonly referred to as featurization.
Edit intent: clarity
Original:  The most success to date has come from finding methods for turning persistence diagrams into vectors in \mathbb{R in a way which preserves as much of the space of persistence diagrams as possible, commonly referred to as featurization.
Revised:  The most success to date has come from finding methods for turning persistence diagrams into \mathbb{R in a way which preserves as much of the space of persistence diagrams as possible, commonly referred to as featurization.
Edit intent: clarity
Original:  The most success to date has come from finding methods for turning persistence diagrams into vectors in \mathbb{R in a way which preserves as much of the space of persistence diagrams as possible, commonly referred to as featurization.
Revised:  The most success to date has come from finding methods for turning persistence diagrams into vectors in \mathbb{R in a way which maximizes the structure preserved. This process is commonly referred to as featurization.
Edit intent: clarity
Original:  We discuss two example realizationsof these functions : tent functions and Chybeyshev interpolating polynomials. Both of these functions are defined on a grid superposed on the birth-lifetime plane. We then combine the resulting features with machine learning algorithms to perform supervised classification and regression on several example data sets, including manifold data, shape data , and an embedded time series from a Rossler system.
Revised:  We discuss two example realizationsof these functions : tent functions , which emphasize the local contributions of points in a persistence diagram, and interpolating polynomials, which capture global pairwise interactions. We combine the resulting features with machine learning algorithms to perform supervised classification and regression on several example data sets, including manifold data, shape data , and an embedded time series from a Rossler system.
Edit intent: meaning-changed
Original:  One counter-intuitive observation is that in most cases using interpolating polynomials, where each point contributes globally to the feature vector, yields significantly better results than using tent functions, where the contribution of each point is localized to its grid cell .
Revised:  One counter-intuitive observation is that in most cases using interpolating polynomials, where each point contributes globally to the feature vector, yields significantly better results than using tent functions, where the contribution of each point is localized .
Edit intent: clarity
Original:  Here, we revisited population genetics data on 165 meadows of four seagrass species in light of recent theoretical developments,
Revised:  Recent modelling approaches have described the expected distributions of genotypic and genetic descriptors under increasing clonal rates. Here, in light of these recent theoretical developments, we revisited population genetics data on 165 meadows of four seagrass species in light of recent theoretical developments,
Edit intent: meaning-changed
Original:  Here, we revisited population genetics data on 165 meadows of four seagrass species in light of recent theoretical developments, which provide new expectations for the distributions of genotypic and genetic polymorphism under increasing clonal rates . Contrasting shoot life span and rhizome turnover lead to the prediction of a decreasing influence of asexual reproduction  along a gradient from Posidonia oceanica to Cymodocea nodosa, Zostera marinaand Zostera noltii , which should be reflected by decreasing departure from Hardy-Weinberg equilibrium (Fis) and increasing genotypic diversity (R).
Revised:  Here, we revisited population genetics data on 165 meadows of four seagrass species . Contrasting shoot life span and rhizome turnover lead to the prediction of a decreasing influence of asexual reproduction along a gradient from Posidonia oceanica to Cymodocea nodosa, Zostera marinaand Zostera noltii , which should be reflected by decreasing departure from Hardy-Weinberg equilibrium (Fis) and increasing genotypic diversity (R).
Edit intent: clarity
Original:  which provide new expectations for the distributions of genotypic and genetic polymorphism under increasing clonal rates . Contrasting shoot life span and rhizome turnover lead to the prediction of a decreasing influence of asexual reproduction  along a gradient from Posidonia oceanica to Cymodocea nodosa, Zostera marinaand Zostera noltii , which should be reflected by decreasing departure from Hardy-Weinberg equilibrium (Fis) and increasing genotypic diversity (R).
Revised:  which provide new expectations for the distributions of genotypic and genetic polymorphism under increasing clonal rates . Contrasting shoot life span and rhizome turnover led to the prediction of a decreasing influence of asexual reproduction along a gradient from Posidonia oceanica to Cymodocea nodosa, Zostera marinaand Zostera noltii , which should be reflected by decreasing departure from Hardy-Weinberg equilibrium (Fis) and increasing genotypic diversity (R).
Edit intent: fluency