wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Our work offers a suite of geometric measures to represent a notion of efficient coding for higher-order cognitive processes, and provide insight into the dimensionality of neural responses characteristic of the successful optimization of reward, that are applicable to the study of cognitive performance more broadly.
Revised:  Our work offers a suite of geometric measures to represent a notion of efficient coding for higher-order cognitive processes, and provide insight into the dimensionality of neural responses characteristic of the successful optimization of reward, that are applicable to the study of efficient coding in higher-order cognitive processes more broadly.
Edit intent: clarity
Original: A fundamental cognitive process is the ability to map objects into meaningful categories depending on the task at hand . Exactly how such mental constructs emerge and what kind of space best embeds this mapping remains incompletely understood.
Revised: A fundamental cognitive process is the ability to map value and identity onto objects as we learn about them . Exactly how such mental constructs emerge and what kind of space best embeds this mapping remains incompletely understood.
Edit intent: meaning-changed
Original:  Lastly, we investigate the neurophysiological drivers of high dimensional patterns at both regional and voxel levels, and  complete our study with a complementary test of the distinguishability of associated whole-brain responses.
Revised:  Lastly, we investigate the neurophysiological drivers of high dimensional patterns at both regional and voxel levels, and we complete our study with a complementary test of the distinguishability of associated whole-brain responses.
Edit intent: fluency
Original: We analyse the valuation and exercise of an American executive call option written on a stock whose drift parameter falls to a lower value at a change point given by an exponential random time , independent of the Brownian motion driving the stock.
Revised: We analyse the optimal exercise of an American executive call option written on a stock whose drift parameter falls to a lower value at a change point given by an exponential random time , independent of the Brownian motion driving the stock.
Edit intent: clarity
Original: We analyse the valuation and exercise of an American executive call option written on a stock whose drift parameter falls to a lower value at a change point given by an exponential random time , independent of the Brownian motion driving the stock.
Revised: We analyse the valuation and exercise of an American call ESO written on a stock whose drift parameter falls to a lower value at a change point given by an exponential random time , independent of the Brownian motion driving the stock.
Edit intent: clarity
Original: We analyse the valuation and exercise of an American executive call option written on a stock whose drift parameter falls to a lower value at a change point given by an exponential random time , independent of the Brownian motion driving the stock.
Revised: We analyse the valuation and exercise of an American executive call option written on a stock whose drift parameter falls to a lower value at a change point given by an exponential random time ,, an exponentially distributed random time independent of the Brownian motion driving the stock.
Edit intent: meaning-changed
Original:  Our setup captures the position of an executive (insider) and employee (outsider), who receive executive stock options. The latter yields a model under the observation filtration %DIFDELCMD < \mathbb F %%% where the drift process \mathbb{F}  becomes a diffusion driven by the innovations process, an %DIFDELCMD < \mathbb F%%% \mathbb{F} -Brownian motion also driving the stock under %DIFDELCMD < \mathbb F%%% \widehat{\mathbb{F}} , and the partial information optimal stopping problem has two spatial dimensions.
Revised:  This scenario is designed to mimic the positions of two employees of varying seniority, a fully informed executive and a partially informed less senior employee, each of whom receives an ESO. The partial information scenario yields a model under the observation filtration %DIFDELCMD < \mathbb F %%% where the drift process \mathbb{F} becomes a diffusion driven by the innovations process, an %DIFDELCMD < \mathbb F%%% \mathbb{F} -Brownian motion also driving the stock under %DIFDELCMD < \mathbb F%%% \widehat{\mathbb{F}} , and the partial information optimal stopping problem has two spatial dimensions.
Edit intent: clarity
Original:  The latter yields a model under the observation filtration %DIFDELCMD < \mathbb F %%% where the drift process \mathbb{F}  becomes a diffusion driven by the innovations process, an %DIFDELCMD < \mathbb F%%% \mathbb{F} -Brownian motion also driving the stock under %DIFDELCMD < \mathbb F%%% \widehat{\mathbb{F}} , and the partial information optimal stopping problem has two spatial dimensions.
Revised:  The latter yields a model under the observation filtration %DIFDELCMD < \mathbb F %%% \mathbb{F} becomes a diffusion driven by the innovations process, an %DIFDELCMD < \mathbb F%%% \mathbb{F} -Brownian motion also driving the stock under %DIFDELCMD < \mathbb F%%% \widehat{\mathbb{F}} , and the partial information optimal stopping problem has two spatial dimensions.
Edit intent: coherence
Original:  The latter yields a model under the observation filtration %DIFDELCMD < \mathbb F %%% where the drift process \mathbb{F}  becomes a diffusion driven by the innovations process, an %DIFDELCMD < \mathbb F%%% \mathbb{F} -Brownian motion also driving the stock under %DIFDELCMD < \mathbb F%%% \widehat{\mathbb{F}} , and the partial information optimal stopping problem has two spatial dimensions.
Revised:  The latter yields a model under the observation filtration %DIFDELCMD < \mathbb F %%% where the drift process \mathbb{F} in which the stock drift becomes a diffusion driven by the innovations process, an %DIFDELCMD < \mathbb F%%% \mathbb{F} -Brownian motion also driving the stock under %DIFDELCMD < \mathbb F%%% \widehat{\mathbb{F}} , and the partial information optimal stopping problem has two spatial dimensions.
Edit intent: clarity
Original:  The latter yields a model under the observation filtration %DIFDELCMD < \mathbb F %%% where the drift process \mathbb{F}  becomes a diffusion driven by the innovations process, an %DIFDELCMD < \mathbb F%%% \mathbb{F} -Brownian motion also driving the stock under %DIFDELCMD < \mathbb F%%% \widehat{\mathbb{F}} , and the partial information optimal stopping problem has two spatial dimensions.
Revised:  The latter yields a model under the observation filtration %DIFDELCMD < \mathbb F %%% where the drift process \mathbb{F} becomes a diffusion driven by the innovations process, an %DIFDELCMD < \mathbb F%%% \mathbb{F} -Brownian motion also driving the stock under %DIFDELCMD < \mathbb F%%% \widehat{\mathbb{F}} , and the partial information optimal stopping value function has two spatial dimensions.
Edit intent: clarity
Original:  We analyse and numerically solve to value the option for both agentsand illustrate that the additional information of the insider can result in exercise patterns which exploit the information on the change point  .
Revised:  We rigorously characterise the free boundary PDEs for both agents, establish shape and regularity properties of the associated optimal exercise boundaries, and prove the smooth pasting property in both information scenarios, exploiting some stochastic flow ideas to do so in the partial information case. We develop finite difference algorithms to numerically solve both agents' exercise and valuation problems and illustrate that the additional information of the insider can result in exercise patterns which exploit the information on the change point .
Edit intent: meaning-changed
Original:  We analyse and numerically solve to value the option for both agentsand illustrate that the additional information of the insider can result in exercise patterns which exploit the information on the change point  .
Revised:  We analyse and numerically solve to value the option for both agentsand illustrate that the additional information of the insider can result in exercise patterns which exploit the information on the change point , lending credence to empirical studies which suggest that privileged information of bad news is a factor leading to early exercise of ESOs prior to poor stock price performance .
Edit intent: meaning-changed
Original: We analyse the optimal exercise of an American call ESO written on a stock whose drift parameter falls to a lower value at a change point , an exponentially distributed random time independent of the Brownian motion driving the stock.
Revised: We analyse the optimal exercise of an executive stock option (ESO) written on a stock whose drift parameter falls to a lower value at a change point , an exponentially distributed random time independent of the Brownian motion driving the stock.
Edit intent: meaning-changed
Original: We analyse the optimal exercise of an American call ESO written on a stock whose drift parameter falls to a lower value at a change point , an exponentially distributed random time independent of the Brownian motion driving the stock.
Revised: We analyse the optimal exercise of an American call ESO written on a stock whose drift parameter falls to a lower value at a change point , an exponentially distributed random time independent of the Brownian motion driving the stock.
Edit intent: fluency
Original: The response time of jobs with multiple parallel tasks  is a critical performance metric in many systems, including MapReduce systems, coded data storage systems, etc. However, tight analytical characterizations of the response time of such jobs are largely unknown except for highly degenerate cases. The difficulty is rooted in the fact that a job with multiple tasks is considered complete only when all of its tasks complete processing;
Revised: The response time of jobs with multiple parallel tasks is a critical performance metric in a wide range of applications such as data file retrieval in coded storage systems and parallel computing. In this problem, each job is completed only when all of its tasks complete processing;
Edit intent: meaning-changed
Original:  The difficulty is rooted in the fact that a job with multiple tasks is considered complete only when all of its tasks complete processing; i.e., the job response time is the maximum of the response times of its tasks  , which is hard to analyze since these task response times are generally not independent.
Revised:  The difficulty is rooted in the fact that a job with multiple tasks is considered complete only when all of its tasks are completed, so the delay of a job is the maximum of the response times of its tasks , which is hard to analyze since these task response times are generally not independent.
Edit intent: clarity
Original:  i.e., the job response time is the maximum of the response times of its tasks  , which is hard to analyze since these task response times are generally not independent.
Revised:  i.e., the job response time is the maximum of the response times of its tasks . Despite the wide attention this problem has received, tight analysis is still largely unknown since analyzing job delay requires characterizing the complicated correlation among task delays, which is hard to do. We first consider an asymptotic regime where the number of servers, n , which is hard to analyze since these task response times are generally not independent.
Edit intent: meaning-changed
Original:  i.e., the job response time is the maximum of the response times of its tasks  , which is hard to analyze since these task response times are generally not independent. In this paper, we approach this problem by studying when the response times of a job's tasks are close to being independent. We consider a limited fork-join model with n servers, where each job consists of k ^{(n)} %DIFDELCMD < \le %%% ntasks.
Revised:  i.e., the job response time is the maximum of the response times of its tasks , goes to infinity, and the number of tasks in a job, k^{(n) ^{(n)} %DIFDELCMD < \le %%% ntasks.
Edit intent: meaning-changed
Original:  We consider a limited fork-join model with n servers, where each job consists of k ^{(n)} %DIFDELCMD < \le %%% ntasks. Upon arrival, each jobchooses k^{(n) under the condition k^{(n)} = o(n^{1/4}) , the steady state response times at any k^{(n) greatly generalizes the asymptotic-independence type of results in the literature where asymptotic independence is shown only for a fixed constant number of queues.
Revised:  We consider a limited fork-join model with n servers, where each job consists of k ^{(n)} %DIFDELCMD < \le %%% queues under the condition k^{(n)} = o(n^{1/4}) , the steady state response times at any k^{(n) greatly generalizes the asymptotic-independence type of results in the literature where asymptotic independence is shown only for a fixed constant number of queues.
Edit intent: clarity
Original:  Upon arrival, each jobchooses k^{(n) under the condition k^{(n)} = o(n^{1/4}) , the steady state response times at any k^{(n) greatly generalizes the asymptotic-independence type of results in the literature where asymptotic independence is shown only for a fixed constant number of queues.
Revised:  Upon arrival, each jobchooses k^{(n) under the condition k^{(n)} = o(n^{1/4}) . This greatly generalizes the asymptotic-independence type of results in the literature where asymptotic independence is shown only for a fixed constant number of queues.
Edit intent: coherence
Original:  We then further show that the job response time converges to the maximum of independent task response times, in a proper sense. This gives the first asymptotically tight analytical characterization of the response time of a multi-task parallel job. To complement the asymptotic independence result, we also show that when k^{(n) =\Theta(n), any number of multiple queues are not asymptotically independent.
Revised:  We then further show that the job response time converges to the maximum of independent task =\Theta(n), any number of multiple queues are not asymptotically independent.
Edit intent: clarity
Original:  Analysis for the regime of k}  ^{(n)} between o(n^{1/4) and \Theta(n) remains open} \le  .
Revised:  Analysis for the regime of k} delays. We next consider the non-asymptotic regime. Here we prove that independence yields a stochastic upper bound on job delay for any n and any k^{(n) ^{(n)} between o(n^{1/4) and \Theta(n) remains open} \le .
Edit intent: meaning-changed
Original:  Analysis for the regime of k}  ^{(n)} between o(n^{1/4) and \Theta(n) remains open} \le  .
Revised:  Analysis for the regime of k} ^{(n)} between o(n^{1/4) and \Theta(n) remains open} \le n. The key component of our proof is a new technique we develop, called "Poisson oversampling". Our approach converts the job delay problem into a corresponding balls-and-bins problem. However, in contrast with typical balls-and-bins problems where there is a negative correlation among bins, we prove that our variant exhibits positive correlation .
Edit intent: meaning-changed
Original:  In this paper, we answer those two remaining questions. We adapt the gadgets of King and Krohn to rectilinear terrains in order to prove that even Orthogonal Terrain Guarding is NP-complete.
Revised:  In this paper, we adapt the gadgets of King and Krohn to rectilinear terrains in order to prove that even Orthogonal Terrain Guarding is NP-complete.
Edit intent: coherence
Original:  Then, we show how their reduction from Planar 3-SAT (as well as our adaptation for rectilinear terrains) can actually be made linear (instead of quadratic) .
Revised:  Then, we show how to obtain an improved ETH lower bound of 2^{\Omega(n^{1/3 reduction from Planar 3-SAT (as well as our adaptation for rectilinear terrains) can actually be made linear (instead of quadratic) .
Edit intent: meaning-changed
Original:  Then, we show how their reduction from Planar 3-SAT (as well as our adaptation for rectilinear terrains) can actually be made linear (instead of quadratic) .
Revised:  Then, we show how their reduction from Planar 3-SAT into a cubic reduction from 3-SAT. This works for both Orthogonal Terrain Guarding and Terrain Guarding .
Edit intent: meaning-changed
Original:  To overcome this bottleneck, we present the REinforcement learning based Adaptive samPling (REAP) algorithm that aims to sample a landscape faster than conventional simulation methods by identifying reaction coordinates that are relevant for sampling the system .
Revised:  To overcome this bottleneck, we present the REinforcement learning based Adaptive samPling (REAP) algorithm that aims to efficiently sample conformational space by learning the relative importance of each reaction coordinate as it samples the landscape .
Edit intent: clarity
Original:  To achieve this, the algorithm uses concepts from the field of reinforcement learning ( a subset of machine learning ) , which rewards sampling along important degrees of freedom and disregards others that do not facilitate exploration or exploitation.
Revised:  To achieve this, the algorithm uses concepts from the field of reinforcement learning , a subset of machine learning ) , which rewards sampling along important degrees of freedom and disregards others that do not facilitate exploration or exploitation.
Edit intent: fluency
Original:  To achieve this, the algorithm uses concepts from the field of reinforcement learning ( a subset of machine learning ) , which rewards sampling along important degrees of freedom and disregards others that do not facilitate exploration or exploitation.
Revised:  To achieve this, the algorithm uses concepts from the field of reinforcement learning ( a subset of machine learning , which rewards sampling along important degrees of freedom and disregards others that do not facilitate exploration or exploitation.
Edit intent: fluency
Original:  We demonstrate the effectiveness of REAP by comparing the sampling to long continuous MD simulations and least-counts adaptive sampling on two model landscapes (L-shaped and circular) . We also demonstrate that the algorithm can be extended to more realistic systems such as alanine dipeptide and Src kinase.
Revised:  We demonstrate the effectiveness of REAP by comparing the sampling to long continuous MD simulations and least-counts adaptive sampling on two model landscapes (L-shaped and circular) , and realistic systems such as alanine dipeptide and Src kinase.
Edit intent: clarity
Original:  In all four systems, the REAP algorithm outperforms the conventional single long trajectory simulation approach as it is able to consistently discover more states as a function of simulation time .
Revised:  In all four systems, the REAP algorithm consistently demonstrates its ability to explore conformational space faster than the other two methods when comparing the expected values of the landscape discovered for a given amount of time. The key advantage of REAP is on-the-fly estimation of the importance of collective variables, which makes it particularly useful for systems with limited structural information .
Edit intent: meaning-changed
Original: Given a set of points P in L_2 , the classic Unit Covering (UC) problem asks to compute the minimum number of unit disks (possibly intersecting) required to cover the points in P, along with a placement of the disks.
Revised: Given a set of points P in the plane , the classic Unit Covering (UC) problem asks to compute the minimum number of unit disks (possibly intersecting) required to cover the points in P, along with a placement of the disks.
Edit intent: meaning-changed
Original:   We show that competitive ratio of an optimal deterministic online algorithm for OUC is at least 3 and at most 5. 
Revised:  We show that competitive ratio of an optimal deterministic online algorithm for OUC is at least 3 and at most 5. Furthermore, we show that for the input point sequences which are subsets of the infinite square or hexagonal lattices, competitive ratio of an optimal deterministic online algorithm for OUC is at least 2.5 and at most 3. The lower bounds derived in this paper are independent of computational complexity.
Edit intent: meaning-changed
Original:  Given a set of points P in the plane, the classic Unit Covering (UC) problem asks to compute the minimum number of unit disks (possibly intersecting) required to cover the points in P, along with a placement of the disks .
Revised: We revisit the online Unit Covering problem in higher dimensions: Given a set of points P in the plane, the classic Unit Covering (UC) problem asks to compute the minimum number of unit disks (possibly intersecting) required to cover the points in P, along with a placement of the disks .
Edit intent: meaning-changed
Original:  In this paper, we study an online version of UC in L_2, which we call as Online Unit Covering (OUC)in L_2, or, simply Online Unit Covering (OUC). In OUC, the points arrive online sequentially. Once a point p arrives, a decision needs to be taken - either assign p to a previously placed disk (if possible)or place a new disk to cover p since none of the previously placed disks can cover p. In this setup, once a disk is placed, its placement cannot be altered in future. Also, the points remain at their places forever.
Revised:  In this paper, we work in \mathbb{R
Edit intent: meaning-changed
Original:  We show that  competitive ratio of an optimal deterministic online algorithm for OUC is at least 3 and at most 5. Furthermore, we show that for the input point sequences which are subsets of the infinite square or hexagonal lattices, / \log{\log{d}}), due to Charikar et al. (2004).
Revised:  We show that competitive ratio of an optimal deterministic online algorithm for OUC is at least d+1 for every d \geq 1. This greatly improves upon the previous best lower bound, \Omega(\log{d / \log{\log{d}}), due to Charikar et al. (2004).
Edit intent: meaning-changed
Original:  (III) We obtain lower bounds of 4 and 5 for the } competitive ratio of an optimal deterministic online algorithm for OUC is at least 2.5 and at most^2 and respectively \mathbb{R}^3;
Revised:  (III) We obtain lower bounds of 4 and 5 for the } competitive ratio of any deterministic algorithm for online Unit Covering in \mathbb{R^2 and respectively \mathbb{R}^3;
Edit intent: clarity
Original: A numerical model that quantitatively describes how platelets in a shear flow adhere and aggregate on a deposition surface has been recently developed in Chopard et al. (2015);
Revised: Recent studies show the existing clinical tests to detect Cardio/cerebrovascular diseases (CVD) are ineffectual as they do not consider different stages of platelet activation or the molecular dynamics involved in platelet interactions. Further they are also incapable to consider inter-individual variability. A physical description of platelets deposition was introduced recently in Chopard et al. (2015);
Edit intent: meaning-changed
Original: A numerical model that quantitatively describes how platelets in a shear flow adhere and aggregate on a deposition surface has been recently developed in Chopard et al. (2015); Chopard et al. ( 2017 ).
Revised: A numerical model that quantitatively describes how platelets in a shear flow adhere and aggregate on a deposition surface has been recently developed in Chopard et . al. 2017 ).
Edit intent: coherence
Original:  Chopard et al. ( 2017 ). Five parameters specify the deposition process and are relevant for a biomedical understanding of the phenomena.
Revised:  Chopard et al. ( 2017 , by integrating fundamental understandings of how platelets interact in a numerical model, parameterized by five parameters. These parameters specify the deposition process and are relevant for a biomedical understanding of the phenomena.
Edit intent: meaning-changed