wanyu/IteraTeR_v2 huggingface dataset:
Original:  Given a collection of points containing many%DIFDELCMD < {\em %%% protected groups , the goal is to find good clustering solutions where each cluster%DIFDELCMD < {\em %%% fairly represents each group.
Revised:  Given a collection of points containing many%DIFDELCMD < {\em %%% , the goal is to find good clustering solutions where each cluster%DIFDELCMD < {\em %%% fairly represents each group.
Edit intent: clarity
Original:  Given a collection of points containing many%DIFDELCMD < {\em %%% protected groups , the goal is to find good clustering solutions where each cluster%DIFDELCMD < {\em %%% fairly represents each group.
Revised:  Given a collection of points containing many%DIFDELCMD < {\em %%% protected groups %DIFDELCMD < {\em %%% fairly represents each group.
Edit intent: clarity
Original:  Given a collection of points containing many%DIFDELCMD < {\em %%% protected groups , the goal is to find good clustering solutions where each cluster%DIFDELCMD < {\em %%% fairly represents each group.
Revised:  Given a collection of points containing many%DIFDELCMD < {\em %%% protected groups , the goal is to find good clustering solutions where each cluster%DIFDELCMD < {\em %%% each group.
Edit intent: clarity
Original:  Our main result is a simple algorithm that, for any \ell_p-norm including the k-center , k-median, and k-means objectives, transforms any clustering solution to a fair one with only a slight loss in quality  .
Revised:  Our main result is a simple algorithm that, for any \ell_p-norm objective (e.g. k-means , k-median, and k-means objectives, transforms any clustering solution to a fair one with only a slight loss in quality .
Edit intent: clarity
Original:  Our main result is a simple algorithm that, for any \ell_p-norm including the k-center , k-median, and k-means objectives, transforms any clustering solution to a fair one with only a slight loss in quality  .
Revised:  Our main result is a simple algorithm that, for any \ell_p-norm including the k-center , k-median, and k-means objectives, transforms any clustering solution to a fair one incurring only a slight loss in quality .
Edit intent: clarity
Original:  The high order field can then be exploited to accurately find irregular points, and accurately integrated using a high order streamline integration method to avoid features like limit cycles.
Revised:  The high order field can then be exploited to accurately find irregular nodes, and can be accurately integrated using a high order streamline integration method to avoid features like limit cycles.
Edit intent: clarity
Original: In quantum compilation , one step translates a technology-independent quantum circuit into a technology-dependent quantum circuit for a targeted device.
Revised: A critical step in quantum compilation is the transformation of a technology-independent quantum circuit into a technology-dependent quantum circuit for a targeted device.
Edit intent: clarity
Original: In quantum compilation , one step translates a technology-independent quantum circuit into a technology-dependent quantum circuit for a targeted device.
Revised: In quantum compilation , one step translates a technology-independent quantum circuit into a technology-dependent form for a targeted device.
Edit intent: clarity
Original:  Besides mapping quantum gates into the supported gate set, it is necessary to map pseudo qubits in the technology-independent circuit into physical qubits of the technology-dependent circuit such that coupling constraints among qubits acting in multiple-qubit gates are satisfied.
Revised:  In addition to mapping quantum gates into the supported gate set, it is necessary to map pseudo qubits in the technology-independent circuit into physical qubits of the technology-dependent circuit such that coupling constraints among qubits acting in multiple-qubit gates are satisfied.
Edit intent: clarity
Original:  To cope with the technical limitations of NISQ-era quantum devices, it is crucial to find a mapping that requires as few additional gates as possible.
Revised:  To cope with the technical limitations of NISQ-era quantum devices, it is advantageous to find a mapping that requires as few additional gates as possible.
Edit intent: clarity
Original:  By means of two examples , we demonstrate how zero-suppressed decision diagrams (ZDDs) can be used for typical implementation tasks in  mapping algorithms.
Revised:  In this work , we demonstrate how zero-suppressed decision diagrams (ZDDs) can be used for typical implementation tasks in mapping algorithms.
Edit intent: clarity
Original:  First, we show how to maximally partition a quantum circuit into blocks of adjacent gates, such that each block can be mapped into a target device without additional SWAP gates.
Revised:  We show how to maximally partition a quantum circuit into blocks of adjacent gates, such that each block can be mapped into a target device without additional SWAP gates.
Edit intent: coherence
Original: We consider assignment policies that allocate resources to requesting users, where everyone is located on a one-dimensional line.
Revised: We consider assignment policies that allocate resources to users, where everyone is located on a one-dimensional line.
Edit intent: clarity
Original: We consider assignment policies that allocate resources to requesting users, where everyone is located on a one-dimensional line.
Revised: We consider assignment policies that allocate resources to requesting users, where both resources and users are located on a one-dimensional line.
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 , we show that they are equivalent with respect to the expected distance traveled by a request (request distance), although MTR is fairer.
Edit intent: clarity
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:  We also consider bidirectional policies 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: clarity
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:  We also consider the bidirectional problem where there are no directional restrictions on resource allocation and develop an algorithm for computing the optimal assignment which is more efficient than known algorithms in literature in resource rich regimes .
Edit intent: clarity
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:  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 the literature when there are more resources than users .
Edit intent: clarity
Original:  Finally, numerical evaluation of performance of unidirectional and bidirectional allocation schemes yield design guidelines beneficial for resource placement.
Revised:  Finally, numerical evaluation of performance of unidirectional and bidirectional allocation schemes yields design guidelines beneficial for resource placement.
Edit intent: fluency
Original:  To this end, the single/multi-commodity maximum flow problems are formulated and the weighted Cheeger constant is adopted as a criteria to improve the maximum flow of the ABS network.
Revised:  To this end, the single/multi-commodity maximum flow problems are formulated and the weighted Cheeger constant is adopted as a criterion to improve the maximum flow of the ABS network.
Edit intent: fluency
Original:  Furthermore, the survey highlights  current challenges and areas of improvement present within the field of research.
Revised:  Furthermore, the survey highlights the current challenges and areas of improvement present within the field of research.
Edit intent: fluency
Original:  It searches dynamic program traces of the host program for points where the dynamic state satisfies a bug template's preconditions and modifies related host program 's code to inject a bug based on the template.
Revised:  It runs tests on the host program for points where the dynamic state satisfies a bug template's preconditions and modifies related host program 's code to inject a bug based on the template.
Edit intent: clarity
Original:  It searches dynamic program traces of the host program for points where the dynamic state satisfies a bug template's preconditions and modifies related host program 's code to inject a bug based on the template.
Revised:  It searches dynamic program traces of the host program to collect dynamic traces, searches the traces for a point where the state satisfies the preconditions for some bug template, then modifies the host program to inject a bug based on the template.
Edit intent: clarity
Original:  Every generated test case is accompanied by a program input whose trace has been shown to contain a dynamically-observed state triggering the injected bug.
Revised:  Every generated test case is accompanied by a program input that exercises the injected bug.
Edit intent: clarity
Original:  This approach allows us to generate on-demand test suites that meet a broad range of requirements and desiderata for bug benchmarks that we have identified .
Revised:  We have identified a broad range of requirements and desiderata for bug benchmarks that we have identified .
Edit intent: clarity
Original:  This approach allows us to generate on-demand test suites that meet a broad range of requirements and desiderata for bug benchmarks that we have identified .
Revised:  This approach allows us to generate on-demand test suites that meet a broad range of requirements and desiderata for bug benchmarks ; our approach generates on-demand test benchmarks that meet these requirements .
Edit intent: clarity
Original:  It also allows us to create customized benchmarks suitable for evaluating tools for a specific use case ( i.e. , a given codebase and  bug types).
Revised:  It also allows us to create customized benchmarks suitable for evaluating tools for a specific use case ( e.g. , a given codebase and bug types).
Edit intent: fluency
Original:  It also allows us to create customized benchmarks suitable for evaluating tools for a specific use case ( i.e. , a given codebase and  bug types).
Revised:  It also allows us to create customized benchmarks suitable for evaluating tools for a specific use case ( i.e. , a given codebase and set of bug types).
Edit intent: clarity
Original:  Our experimental evaluation demonstrates the suitability of our generated test suites for evaluating static bug-detection tools and for comparing the performance of multiple tools.
Revised:  Our experimental evaluation demonstrates the suitability of our generated benchmark for evaluating static bug-detection tools and for comparing the performance of multiple tools.
Edit intent: clarity
Original:  Our experimental evaluation demonstrates the suitability of our generated test suites for evaluating static bug-detection tools and for comparing the performance of multiple tools.
Revised:  Our experimental evaluation demonstrates the suitability of our generated test suites for evaluating static bug-detection tools and for comparing the performance of different tools.
Edit intent: clarity
Original:  In this paper, we study a more refined complexity by taking into account the "lingering" of gradients: once a gradient is computed at x_k, the additional time to compute gradients at x_{k+1},x_{k+2},\dots may be reduced.
Revised:  In this paper, we study a more refined complexity by taking into account the `lingering' of gradients: once a gradient is computed at x_k, the additional time to compute gradients at x_{k+1},x_{k+2},\dots may be reduced.
Edit intent: fluency
Original:  We show how this improves the running time of gradient descent and SVRG . For instance, if the "additional time" scales linearly with respect to the traveled distance, then the "convergence rate" of gradient descent can be improved from 1/T to \exp(-T^{1/3}).
Revised:  We show how this improves the running time of gradient descent and SVRG . For instance, if the `additional time' scales linearly with respect to the traveled distance, then the "convergence rate" of gradient descent can be improved from 1/T to \exp(-T^{1/3}).
Edit intent: fluency
Original:  We show how this improves the running time of gradient descent and SVRG . For instance, if the "additional time" scales linearly with respect to the traveled distance, then the "convergence rate" of gradient descent can be improved from 1/T to \exp(-T^{1/3}).
Revised:  We show how this improves the running time of gradient descent and SVRG . For instance, if the "additional time" scales linearly with respect to the traveled distance, then the `convergence rate' of gradient descent can be improved from 1/T to \exp(-T^{1/3}).
Edit intent: fluency
Original:  Front Page Today Module application with 4.6m users to 10^{-6} error (or 10^{-12 6 passes of the dataset  .
Revised:  Front Page Today Module with 4.6m users to 10^{-6} error (or 10^{-12 6 passes of the dataset .
Edit intent: clarity
Original: The characteristics of the h index in the field of condensed matter physics are studied using high-quality data from ResearcherID.
Revised: The characteristics of the h-index in the field of condensed matter physics are studied using high-quality data from ResearcherID.
Edit intent: fluency
Original:  The results are examined in terms of theoretical descriptions of the h index ' overall dependence on a researcher's total number of published papers, and total number of citations.
Revised:  The results are examined in terms of theoretical descriptions of the h-index ' overall dependence on a researcher's total number of published papers, and total number of citations.
Edit intent: clarity
Original:  A corresponding analysis with similar results is performed using the multi-author h_m index .
Revised:  A corresponding analysis with similar results is performed using the multi-author h_m -index .
Edit intent: clarity
Original:  We demonstrate that a version using orthogonal factorization and block-diagonal scaling takes less CG iterations to converge than previous similar algorithms on various kinds of problems.
Revised:  We demonstrate that a version using orthogonal factorization and block-diagonal scaling takes fewer CG iterations to converge than previous similar algorithms on various kinds of problems.
Edit intent: fluency
Original:  We evaluate the algorithm on some large problems  show it exhibits near-linear scaling.
Revised:  We evaluate the algorithm on some large problems and show it exhibits near-linear scaling.
Edit intent: coherence
Original:  To verify the conjecture of a barrier type optimal control, we first introduce and study an auxiliary problem with the final payoff at an exponential terminal time and characterize the optimal threshold explicitly using fluctuation identities of the refracted-reflected Levy process.
Revised:  To verify the conjecture of a barrier type optimal control, we first introduce and study an auxiliary problem with the final payoff at an exponential terminal time and characterize the optimal threshold explicitly using fluctuation identities of the refracted-reflected L\'evy process.
Edit intent: fluency
Original:  To verify the conjecture of a barrier type optimal control, we first introduce and study an auxiliary problem with the final payoff at an exponential terminal time and characterize the optimal threshold explicitly using fluctuation identities of the refracted-reflected L\'evy process.
Revised:  To verify the conjecture of a barrier type optimal control, we first introduce and study an auxiliary problem with the final payoff at an exponential terminal time and characterize the optimal threshold explicitly using fluctuation identities of the refracted-reflected Levy process.
Edit intent: fluency
Original:  In this paper, we focus on a network represented by a regular tree which does not have any cycle , and all nodes have the same number of edges connected to a node.
Revised:  In this paper, we focus on a network represented by a regular tree which does not have any cycle and in which all nodes have the same number of edges connected to a node.
Edit intent: coherence
Original:  Introducing a formalism originating from the theory of optimal partial transport, we build a convenient framework to prove topological properties of this new space, which will also hold for the closed subspace of persistence diagrams.
Revised:  We study the topological properties of this new space, which will also hold for the closed subspace of persistence diagrams.
Edit intent: clarity
Original:  We also showcase the strength of this framework  by providing several statistical results made meaningful thanks to this new formalism.
Revised:  We also showcase the usefulness of this framework by providing several statistical results made meaningful thanks to this new formalism.
Edit intent: clarity
Original:  We study the topological properties of this new space, which will also hold for the closed subspace of persistence diagrams.
Revised:  We explore topological properties of this new space, which will also hold for the closed subspace of persistence diagrams.
Edit intent: clarity
Original:  We also showcase the usefulness of this framework to study random persistence diagrams by providing several statistical results made meaningful thanks to this new formalism.
Revised:  We also showcase the strength of this framework to study random persistence diagrams by providing several statistical results made meaningful thanks to this new formalism.
Edit intent: clarity
Original:  Some important properties of this discretization  are proved by its linkage to Volterra integrals with completely monotone kernels.
Revised:  Properties of this discretization are proved by its linkage to Volterra integrals with completely monotone kernels.
Edit intent: clarity
Original:  We then analyze discretization of some time fractional dissipative problems and obtain some interesting results using the backward scheme for this discretization .
Revised:  We then apply the backward scheme corresponding to this discretization to two time fractional dissipative problems and obtain some interesting results using the backward scheme for this discretization .
Edit intent: clarity
Original:  We then analyze discretization of some time fractional dissipative problems and obtain some interesting results using the backward scheme for this discretization .
Revised:  We then analyze discretization of some time fractional dissipative problems , and these implicit schemes are helpful for the analysis of the corresponding problems .
Edit intent: clarity
Original: The plant hormone auxin is regulating many aspects of plant development and one striking dynamical feature is the self-organisation of leaf venation patterns  driven by high  auxin within vein cells and a facilitated transport of auxin mediated by specialised membrane-localised proteins.
Revised: The plant hormone auxin controls many aspects of plant development and one striking dynamical feature is the self-organisation of leaf venation patterns driven by high auxin within vein cells and a facilitated transport of auxin mediated by specialised membrane-localised proteins.
Edit intent: clarity
Original: The plant hormone auxin is regulating many aspects of plant development and one striking dynamical feature is the self-organisation of leaf venation patterns  driven by high  auxin within vein cells and a facilitated transport of auxin mediated by specialised membrane-localised proteins.
Revised: The plant hormone auxin is regulating many aspects of the development of plants. One striking dynamical feature is the self-organisation of leaf venation patterns driven by high auxin within vein cells and a facilitated transport of auxin mediated by specialised membrane-localised proteins.
Edit intent: clarity
Original: The plant hormone auxin is regulating many aspects of plant development and one striking dynamical feature is the self-organisation of leaf venation patterns  driven by high  auxin within vein cells and a facilitated transport of auxin mediated by specialised membrane-localised proteins.
Revised: The plant hormone auxin is regulating many aspects of plant development and one striking dynamical feature is the self-organisation of leaf venation patterns which is driven by high auxin within vein cells and a facilitated transport of auxin mediated by specialised membrane-localised proteins.
Edit intent: coherence
Original: The plant hormone auxin is regulating many aspects of plant development and one striking dynamical feature is the self-organisation of leaf venation patterns  driven by high  auxin within vein cells and a facilitated transport of auxin mediated by specialised membrane-localised proteins.
Revised: The plant hormone auxin is regulating many aspects of plant development and one striking dynamical feature is the self-organisation of leaf venation patterns driven by high levels of auxin within vein cells and a facilitated transport of auxin mediated by specialised membrane-localised proteins.
Edit intent: clarity
Original: The plant hormone auxin is regulating many aspects of plant development and one striking dynamical feature is the self-organisation of leaf venation patterns  driven by high  auxin within vein cells and a facilitated transport of auxin mediated by specialised membrane-localised proteins.
Revised: The plant hormone auxin is regulating many aspects of plant development and one striking dynamical feature is the self-organisation of leaf venation patterns driven by high auxin within vein cells . The auxin transport is mediated by specialised membrane-localised proteins.
Edit intent: coherence
Original:  Highly important for correct venation patterns are polarly localised efflux-mediator proteins of the PIN family.
Revised:  Many venation models have been based on polarly localised efflux-mediator proteins of the PIN family.
Edit intent: clarity
Original:  Here, we investigate a model of auxin transport with a positive feedback between auxin fluxes and transport capacities that are not necessarily polar, adapted from a recently proposed model for transport networks.
Revised:  Here, we investigate a modeling framework for auxin transport with a positive feedback between auxin fluxes and transport capacities that are not necessarily polar, adapted from a recently proposed model for transport networks.
Edit intent: clarity
Original:  We show global existence and nonnegativity of solutions to the model , and demonstrate the validity of Murray's law for the steady statesof the model.
Revised:  We show global existence and nonnegativity of solutions to the model and the validity of Murray's law for the steady statesof the model.
Edit intent: coherence