wanyu/IteraTeR_v2 huggingface dataset:
Original:   is the relaxation time of the lazy random walk on G and d is the minimum degree in G. Alternatively, m can be estimated in O}\left( _{ %DIFDELCMD < \rm %%% unif } ^G) ^{ 3 / 4 } ) steps, where t}\right) _{ %DIFDELCMD < \rm %%% unif } ^G is the uniform mixing time on G. The algorithm is based on\left(}\frac{m}{n}}\right)  the number of intersections of random walk paths X,Y, i.e. the number of times (t,s) such that X_t=Y_s.
Revised:  is the relaxation time of the lazy random walk on G and d is the minimum degree in G. Alternatively, m can be estimated in O}\left( _{ %DIFDELCMD < \rm %%% unif } ^G) ^{ 3 / 4 } ) steps, where t}\right) _{ %DIFDELCMD < \rm %%% unif } ^G is the uniform mixing time on G. The algorithm is based on\left(t_{\mathrm{unif}\frac{m}{n}}\right) the number of intersections of random walk paths X,Y, i.e. the number of times (t,s) such that X_t=Y_s.
Edit intent: clarity
Original:   is the relaxation time of the lazy random walk on G and d is the minimum degree in G. Alternatively, m can be estimated in O}\left( _{ %DIFDELCMD < \rm %%% unif } ^G) ^{ 3 / 4 } ) steps, where t}\right) _{ %DIFDELCMD < \rm %%% unif } ^G is the uniform mixing time on G. The algorithm is based on\left(}\frac{m}{n}}\right)  the number of intersections of random walk paths X,Y, i.e. the number of times (t,s) such that X_t=Y_s.
Revised:  is the relaxation time of the lazy random walk on G and d is the minimum degree in G. Alternatively, m can be estimated in O}\left( _{ %DIFDELCMD < \rm %%% unif } ^G) ^{ 3 / 4 } ) steps, where t}\right) _{ %DIFDELCMD < \rm %%% unif } ^G is the uniform mixing time on G. The algorithm is based on\left(}\frac{m}{n}}\right) steps. Our algorithms are based on counting the number of intersections of random walk paths X,Y, i.e. the number of times (t,s) such that X_t=Y_s.
Edit intent: clarity
Original:   is the relaxation time of the lazy random walk on G and d is the minimum degree in G. Alternatively, m can be estimated in O}\left( _{ %DIFDELCMD < \rm %%% unif } ^G) ^{ 3 / 4 } ) steps, where t}\right) _{ %DIFDELCMD < \rm %%% unif } ^G is the uniform mixing time on G. The algorithm is based on\left(}\frac{m}{n}}\right)  the number of intersections of random walk paths X,Y, i.e. the number of times (t,s) such that X_t=Y_s.
Revised:  is the relaxation time of the lazy random walk on G and d is the minimum degree in G. Alternatively, m can be estimated in O}\left( _{ %DIFDELCMD < \rm %%% unif } ^G) ^{ 3 / 4 } ) steps, where t}\right) _{ %DIFDELCMD < \rm %%% unif } ^G is the uniform mixing time on G. The algorithm is based on\left(}\frac{m}{n}}\right) the number of intersections of random walk paths X,Y, i.e. the number of pairs (t,s) such that X_t=Y_s.
Edit intent: clarity
Original:  Our method improves on previous methods by various authors which only consider collisions (i.e.  times t with X_t=Y_t).
Revised:  This improves on previous methods by various authors which only consider collisions (i.e. times t with X_t=Y_t).
Edit intent: fluency
Original:  Our method improves on previous methods by various authors which only consider collisions (i.e.  times t with X_t=Y_t).
Revised:  Our method improves on previous estimates which only consider collisions (i.e. times t with X_t=Y_t).
Edit intent: clarity
Original:  Our method improves on previous methods by various authors which only consider collisions (i.e.  times t with X_t=Y_t).
Revised:  Our method improves on previous methods by various authors which only consider collisions (i.e. , times t with X_t=Y_t).
Edit intent: fluency
Original:  We also show that the time complexity of our algorithm is optimal(up to log factors) for 3-regular graphs with prescribed mixing times.
Revised:  We also show that the complexity of our algorithm is optimal(up to log factors) for 3-regular graphs with prescribed mixing times.
Edit intent: clarity
Original:  On the other hand, we show that, given either m _G or the mixing time of G, we can compute the "other parameter" with a self-stopping algorithm.
Revised:  On the other hand, we show that, given either m or the mixing time of G, we can compute the "other parameter" with a self-stopping algorithm.
Edit intent: clarity
Original: Despite the numerical challenges, finite element method is used for the simulation of viscous fluid flow.
Revised: Despite its numerical challenges, finite element method is used for the simulation of viscous fluid flow.
Edit intent: fluency
Original: Despite the numerical challenges, finite element method is used for the simulation of viscous fluid flow.
Revised: Despite the numerical challenges, finite element method is used to compute viscous fluid flow.
Edit intent: clarity
Original:  We implement and solve the weak form by using open-source packages and present the accuracy by comparing the simulation to the closed-form solutions in the case of a linear viscous fluid.
Revised:  We implement and solve the weak form by using open-source packages and the accuracy as well as the robustness is demonstrated by comparing results to the closed-form solutions in the case of a linear viscous fluid.
Edit intent: clarity
Original:  These stabilization methods are  often applied relative to the element size such that a local monotonous convergence cannot be observed .
Revised:  These stabilization methods are useful; however, they are often applied relative to the element size such that a local monotonous convergence cannot be observed .
Edit intent: coherence
Original:  These stabilization methods are  often applied relative to the element size such that a local monotonous convergence cannot be observed .
Revised:  These stabilization methods are often applied relative to the element size such that a local monotonous convergence is challenging to acquire .
Edit intent: clarity
Original:  We need a computational strategy for solving viscous fluid flow using only the balance equations.
Revised:  We need a computational strategy for solving viscous fluid flow using solely the balance equations.
Edit intent: fluency
Original:  Hence  its generalization to multiphysics applications is straight-forward .
Revised:  Hence , its generalization to multiphysics applications is straight-forward .
Edit intent: fluency
Original:  Hence  its generalization to multiphysics applications is straight-forward .
Revised:  Hence its generalization to multiphysics applications is straightforward .
Edit intent: coherence
Original:  We discuss several numerical problems and present the methodology rigorously.
Revised:  We discuss emerging numerical problems and present the methodology rigorously.
Edit intent: clarity
Original:  Implementation is achieved by using open-source packages and the accuracy as well as the robustness is demonstrated by comparing results to the closed-form solutions and by solving benchmarking problems.
Revised:  Implementation is achieved by using open-source packages and the accuracy as well as the robustness is demonstrated by comparing results to the closed-form solutions and also by solving well-known benchmarking problems.
Edit intent: clarity
Original: This paper studies edge caching in dense heterogeneous cellular networks  , in which small base stations (SBSs) with limited cache size store the popular contents, and massive multiple-input multiple-output (MIMO) aided macro base stations provide wireless self-backhaul when SBSs require the non-cached contents.
Revised: This paper focuses on edge caching in dense heterogeneous cellular networks , in which small base stations (SBSs) with limited cache size store the popular contents, and massive multiple-input multiple-output (MIMO) aided macro base stations provide wireless self-backhaul when SBSs require the non-cached contents.
Edit intent: clarity
Original:  We address the effects of cell load and hit probability on the successful content delivery (SCD), and evaluate the minimum required base station density for avoiding the access overload in a small cell and backhaul overload in a macrocell.
Revised:  Our aim is to address the effects of cell load and hit probability on the successful content delivery (SCD), and evaluate the minimum required base station density for avoiding the access overload in a small cell and backhaul overload in a macrocell.
Edit intent: clarity
Original:  We address the effects of cell load and hit probability on the successful content delivery (SCD), and evaluate the minimum required base station density for avoiding the access overload in a small cell and backhaul overload in a macrocell.
Revised:  We address the effects of cell load and hit probability on the successful content delivery (SCD), and present the minimum required base station density for avoiding the access overload in a small cell and backhaul overload in a macrocell.
Edit intent: clarity
Original:  We address the effects of cell load and hit probability on the successful content delivery (SCD), and evaluate the minimum required base station density for avoiding the access overload in a small cell and backhaul overload in a macrocell.
Revised:  We address the effects of cell load and hit probability on the successful content delivery (SCD), and evaluate the minimum required base station density for avoiding the access overload in an arbitrary small cell and backhaul overload in a macrocell.
Edit intent: clarity
Original:  We derive the massive MIMO backhaul achievable rate without downlink channel estimation , to calculate the backhaul time .
Revised:  We derive the massive MIMO backhaul achievable rate without downlink channel estimation is derived to calculate the backhaul time .
Edit intent: clarity
Original: Unification and generalization are operations on two terms computing respectively their greatest lower bound and least upper bound when the terms are quasi-ordered by subsumption up to variable renaming (i.e., t_1 is subsumed by t_2 iff t_1 = t_2\sigma for some variable substitution \sigma).
Revised: Unification and generalization are operations on two terms computing respectively their greatest lower bound and least upper bound when the terms are quasi-ordered by subsumption up to variable renaming (i.e., t_1 \preceq t_2 iff t_1 = t_2\sigma for some variable substitution \sigma).
Edit intent: clarity
Original:  This allows to literally replace the ambient dimension by an intrinsic notion of dimension related to the structure of the data.
Revised:  We can therefore literally replace the ambient dimension by an intrinsic notion of dimension related to the structure of the data.
Edit intent: coherence
Original:  Here, we improve over those methods with TRaIT, a unified statistical framework for the inference of the accumula- tion order of multiple types of genomic alterations driving tumor development.
Revised:  Here, we improve over those methods with TRaIT, a computational framework to infer mutational graphs that model the accumulation of multiple types of genomic alterations driving tumor development.
Edit intent: clarity
Original:  We show with single-cell data from breast cancer and multi-region data from colorectal cancer that TRaIT can quantify the extent of intra-tumor heterogeneity and generate new testable experimental hypotheses.
Revised:  We show with single-cell and multi-region data from colorectal cancer that TRaIT can quantify the extent of intra-tumor heterogeneity and generate new testable experimental hypotheses.
Edit intent: clarity
Original:  We show with single-cell data from breast cancer and multi-region data from colorectal cancer that TRaIT can quantify the extent of intra-tumor heterogeneity and generate new testable experimental hypotheses.
Revised:  We show with single-cell data from breast cancer and multi-region cancer datasets can produce accurate and reliable models of single-tumour evolution, quantify the extent of intra-tumor heterogeneity and generate new testable experimental hypotheses.
Edit intent: clarity
Original:  We show with single-cell data from breast cancer and multi-region data from colorectal cancer that TRaIT can quantify the extent of intra-tumor heterogeneity and generate new testable experimental hypotheses.
Revised:  We show with single-cell data from breast cancer and multi-region data from colorectal cancer that TRaIT can quantify the extent of intra-tumour heterogeneity and generate new testable experimental hypotheses.
Edit intent: fluency
Original:  Timing results are shown for the code running with MPI-only (up to 1728 CPU cores) and with MPI+OpenACC (up to 64 NVIDIA P100 GPUs ).
Revised:  Timing results are shown for running the code with MPI-only (up to 1728 CPU cores) and with MPI+OpenACC (up to 64 NVIDIA P100 GPUs ).
Edit intent: fluency
Original:  Timing results are shown for the code running with MPI-only (up to 1728 CPU cores) and with MPI+OpenACC (up to 64 NVIDIA P100 GPUs ).
Revised:  Timing results are shown for the code running with MPI-only on multiple CPUs, and with MPI+OpenACC (up to 64 NVIDIA P100 GPUs ).
Edit intent: clarity
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Edit intent: clarity
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% F %DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Edit intent: fluency
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Edit intent: clarity
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L %DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Edit intent: fluency
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Edit intent: fluency
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A %DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Edit intent: clarity
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% F imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Edit intent: fluency
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% Sast imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Edit intent: fluency
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% SL imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Edit intent: fluency
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% SSH imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Edit intent: fluency
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% SA imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Edit intent: fluency
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% Slgorithm for imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Edit intent: fluency
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% SS imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Edit intent: fluency
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Edit intent: fluency
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) ), a similarity search system for ultra-high dimensional datasets on a single machine, that does not require similarity computation.
Edit intent: fluency