wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Given a convex body%DIFDELCMD < \body%%% , via a separation oracle, the algorithm performs a small sequence of (oracle) stabbing queries (computed from%DIFDELCMD < \Net%%% ) -- if none of the query points hits%DIFDELCMD < \body%%% , then%DIFDELCMD < \body %%% contains less than an%DIFDELCMD < \eps%%% -fraction of the input points.
Revised:  %DIFDELCMD < \body%%% , via a separation oracle, the algorithm performs a small sequence of (oracle) stabbing queries (computed from%DIFDELCMD < \Net%%% ) -- if none of the query points hits%DIFDELCMD < \body%%% , then%DIFDELCMD < \body %%% contains less than an%DIFDELCMD < \eps%%% -fraction of the input points.
Edit intent: clarity
Original:  Given a convex body%DIFDELCMD < \body%%% , via a separation oracle, the algorithm performs a small sequence of (oracle) stabbing queries (computed from%DIFDELCMD < \Net%%% ) -- if none of the query points hits%DIFDELCMD < \body%%% , then%DIFDELCMD < \body %%% contains less than an%DIFDELCMD < \eps%%% -fraction of the input points.
Revised:  Given a convex body%DIFDELCMD < \body%%% %DIFDELCMD < \Net%%% ) -- if none of the query points hits%DIFDELCMD < \body%%% , then%DIFDELCMD < \body %%% contains less than an%DIFDELCMD < \eps%%% -fraction of the input points.
Edit intent: clarity
Original:  Given a convex body%DIFDELCMD < \body%%% , via a separation oracle, the algorithm performs a small sequence of (oracle) stabbing queries (computed from%DIFDELCMD < \Net%%% ) -- if none of the query points hits%DIFDELCMD < \body%%% , then%DIFDELCMD < \body %%% contains less than an%DIFDELCMD < \eps%%% -fraction of the input points.
Revised:  Given a convex body%DIFDELCMD < \body%%% , via a separation oracle, the algorithm performs a small sequence of (oracle) stabbing queries (computed from%DIFDELCMD < \Net%%% %DIFDELCMD < \body%%% , then%DIFDELCMD < \body %%% contains less than an%DIFDELCMD < \eps%%% -fraction of the input points.
Edit intent: coherence
Original:  Given a convex body%DIFDELCMD < \body%%% , via a separation oracle, the algorithm performs a small sequence of (oracle) stabbing queries (computed from%DIFDELCMD < \Net%%% ) -- if none of the query points hits%DIFDELCMD < \body%%% , then%DIFDELCMD < \body %%% contains less than an%DIFDELCMD < \eps%%% -fraction of the input points.
Revised:  Given a convex body%DIFDELCMD < \body%%% , via a separation oracle, the algorithm performs a small sequence of (oracle) stabbing queries (computed from%DIFDELCMD < \Net%%% ) -- if none of the query points hits%DIFDELCMD < \body%%% %DIFDELCMD < \body %%% contains less than an%DIFDELCMD < \eps%%% -fraction of the input points.
Edit intent: coherence
Original:  Given a convex body%DIFDELCMD < \body%%% , via a separation oracle, the algorithm performs a small sequence of (oracle) stabbing queries (computed from%DIFDELCMD < \Net%%% ) -- if none of the query points hits%DIFDELCMD < \body%%% , then%DIFDELCMD < \body %%% contains less than an%DIFDELCMD < \eps%%% -fraction of the input points.
Revised:  Given a convex body%DIFDELCMD < \body%%% , via a separation oracle, the algorithm performs a small sequence of (oracle) stabbing queries (computed from%DIFDELCMD < \Net%%% ) -- if none of the query points hits%DIFDELCMD < \body%%% , then%DIFDELCMD < \body %%% %DIFDELCMD < \eps%%% -fraction of the input points.
Edit intent: clarity
Original:  Given a convex body%DIFDELCMD < \body%%% , via a separation oracle, the algorithm performs a small sequence of (oracle) stabbing queries (computed from%DIFDELCMD < \Net%%% ) -- if none of the query points hits%DIFDELCMD < \body%%% , then%DIFDELCMD < \body %%% contains less than an%DIFDELCMD < \eps%%% -fraction of the input points. The number of stabbing queries performed is O( d^2\log%DIFDELCMD < \eps%%% ^{-1 \tldO(d ^9%DIFDELCMD < \eps%%% ^{-1 is the first weak%DIFDELCMD < \eps%%% -net related construction where all constants/bounds are polynomial in the dimension.
Revised:  Given a convex body%DIFDELCMD < \body%%% , via a separation oracle, the algorithm performs a small sequence of (oracle) stabbing queries (computed from%DIFDELCMD < \Net%%% ) -- if none of the query points hits%DIFDELCMD < \body%%% , then%DIFDELCMD < \body %%% contains less than an%DIFDELCMD < \eps%%% %DIFDELCMD < \eps%%% ^{-1 \tldO(d ^9%DIFDELCMD < \eps%%% ^{-1 is the first weak%DIFDELCMD < \eps%%% -net related construction where all constants/bounds are polynomial in the dimension.
Edit intent: meaning-changed
Original:  The number of stabbing queries performed is O( d^2\log%DIFDELCMD < \eps%%% ^{-1 \tldO(d ^9%DIFDELCMD < \eps%%% ^{-1 is the first weak%DIFDELCMD < \eps%%% -net related construction where all constants/bounds are polynomial in the dimension.
Revised:  The number of stabbing queries performed is O( d^2\log%DIFDELCMD < \eps%%% We present an improved algorithm that computes (roughly) a 1/d^2-centerpoint with running time \tldO(d ^9%DIFDELCMD < \eps%%% ^{-1 is the first weak%DIFDELCMD < \eps%%% -net related construction where all constants/bounds are polynomial in the dimension.
Edit intent: meaning-changed
Original:  The number of stabbing queries performed is O( d^2\log%DIFDELCMD < \eps%%% ^{-1 \tldO(d ^9%DIFDELCMD < \eps%%% ^{-1 is the first weak%DIFDELCMD < \eps%%% -net related construction where all constants/bounds are polynomial in the dimension.
Revised:  The number of stabbing queries performed is O( d^2\log%DIFDELCMD < \eps%%% ^{-1 \tldO(d %DIFDELCMD < \eps%%% ^{-1 is the first weak%DIFDELCMD < \eps%%% -net related construction where all constants/bounds are polynomial in the dimension.
Edit intent: fluency
Original:  The number of stabbing queries performed is O( d^2\log%DIFDELCMD < \eps%%% ^{-1 \tldO(d ^9%DIFDELCMD < \eps%%% ^{-1 is the first weak%DIFDELCMD < \eps%%% -net related construction where all constants/bounds are polynomial in the dimension.
Revised:  The number of stabbing queries performed is O( d^2\log%DIFDELCMD < \eps%%% ^{-1 \tldO(d ^9%DIFDELCMD < \eps%%% ^7). While the improvements are (arguably) mild, it is the first weak%DIFDELCMD < \eps%%% -net related construction where all constants/bounds are polynomial in the dimension.
Edit intent: meaning-changed
Original:  The number of stabbing queries performed is O( d^2\log%DIFDELCMD < \eps%%% ^{-1 \tldO(d ^9%DIFDELCMD < \eps%%% ^{-1 is the first weak%DIFDELCMD < \eps%%% -net related construction where all constants/bounds are polynomial in the dimension.
Revised:  The number of stabbing queries performed is O( d^2\log%DIFDELCMD < \eps%%% ^{-1 \tldO(d ^9%DIFDELCMD < \eps%%% ^{-1 is the first %DIFDELCMD < \eps%%% -net related construction where all constants/bounds are polynomial in the dimension.
Edit intent: fluency
Original:  The number of stabbing queries performed is O( d^2\log%DIFDELCMD < \eps%%% ^{-1 \tldO(d ^9%DIFDELCMD < \eps%%% ^{-1 is the first weak%DIFDELCMD < \eps%%% -net related construction where all constants/bounds are polynomial in the dimension. (B) If one is allowed to expand the convex range before checking if it intersects the sample, then a sample of size%DIFDELCMD < \Bigl.\tldO%%% (%DIFDELCMD < \eps%%% ^{-(d+1)/2), from the original point set, is sufficient to form a net.
Revised:  The number of stabbing queries performed is O( d^2\log%DIFDELCMD < \eps%%% ^{-1 \tldO(d ^9%DIFDELCMD < \eps%%% ^{-1 is the first weak%DIFDELCMD < \eps%%% %DIFDELCMD < \Bigl.\tldO%%% (%DIFDELCMD < \eps%%% ^{-(d+1)/2), from the original point set, is sufficient to form a net.
Edit intent: meaning-changed
Original:  (B) If one is allowed to expand the convex range before checking if it intersects the sample, then a sample of size%DIFDELCMD < \Bigl.\tldO%%% (%DIFDELCMD < \eps%%% ^{-(d+1)/2), from the original point set, is sufficient to form a net.
Revised:  (B) If one is allowed to expand the convex range before checking if it intersects the sample, then a sample of size%DIFDELCMD < \Bigl.\tldO%%% %DIFDELCMD < \eps%%% ^{-(d+1)/2), from the original point set, is sufficient to form a net.
Edit intent: fluency
Original:  (B) If one is allowed to expand the convex range before checking if it intersects the sample, then a sample of size%DIFDELCMD < \Bigl.\tldO%%% (%DIFDELCMD < \eps%%% ^{-(d+1)/2), from the original point set, is sufficient to form a net.
Revised:  (B) If one is allowed to expand the convex range before checking if it intersects the sample, then a sample of size%DIFDELCMD < \Bigl.\tldO%%% (%DIFDELCMD < \eps%%% ), from the original point set, is sufficient to form a net.
Edit intent: meaning-changed
Original:  (C) We show a construction of weak }%DIFDELCMD < \eps%%% -nets which have the following additional property: For a heavy body, there is a net point that stabs the body, and it is also a good centerpoint for the points contained inside the body. (D) We present a variant of a known algorithm for approximating a centerpoint, improving the running time from%DIFDELCMD < \tldO%%% (d^9) to%DIFDELCMD < \tldO%%% (d^7).
Revised:  (C) We show a construction of weak }%DIFDELCMD < \eps%%% %DIFDELCMD < \tldO%%% (d^9) to%DIFDELCMD < \tldO%%% (d^7).
Edit intent: coherence
Original:  (D) We present a variant of a known algorithm for approximating a centerpoint, improving the running time from%DIFDELCMD < \tldO%%% (d^9) to%DIFDELCMD < \tldO%%% (d^7).
Revised:  (D) We present a variant of a known algorithm for approximating a centerpoint, improving the running time from%DIFDELCMD < \tldO%%% %DIFDELCMD < \tldO%%% (d^7).
Edit intent: meaning-changed
Original:  (D) We present a variant of a known algorithm for approximating a centerpoint, improving the running time from%DIFDELCMD < \tldO%%% (d^9) to%DIFDELCMD < \tldO%%% (d^7). Our analysis of this algorithmis arguably cleaner than the previous version .
Revised:  (D) We present a variant of a known algorithm for approximating a centerpoint, improving the running time from%DIFDELCMD < \tldO%%% (d^9) to%DIFDELCMD < \tldO%%% progress on this well known problem in over twenty years. The new algorithm is simpler, and the running time bound follows by a simple random walk argument, which we believe to be of independent interest. We also present several new applications of the improved centerpoint algorithm .
Edit intent: meaning-changed
Original: We introduce a Random Attention Model (RAM) allowing for a large class of stochastic consideration maps in the context of an otherwise canonical limited attention model for decision theory.
Revised: This paper illustrates how one can deduce preference from observed choices when attention is not only limited but also random. In contrast to earlier approaches, we introduce a Random Attention Model (RAM) allowing for a large class of stochastic consideration maps in the context of an otherwise canonical limited attention model for decision theory.
Edit intent: meaning-changed
Original: We introduce a Random Attention Model (RAM) allowing for a large class of stochastic consideration maps in the context of an otherwise canonical limited attention model for decision theory. The model relies on a new restriction on the unobserved, possibly stochastic consideration map, termedMonotonic Attention , which is intuitive and nests many recent contributions in the literature on limited attention.
Revised: We introduce a Random Attention Model (RAM) allowing for a large class of Monotonic Attention , which is intuitive and nests many recent contributions in the literature on limited attention.
Edit intent: coherence
Original:  The model relies on a new restriction on the unobserved, possibly stochastic consideration map, termedMonotonic Attention , which is intuitive and nests many recent contributions in the literature on limited attention.
Revised:  The model relies on a new restriction on the unobserved, possibly stochastic consideration map, termedMonotonic Attention nonparametric random attention rules. Our model imposes one intuitive condition, termed Monotonic Attention, which captures the idea that each consideration set competes for the decision-maker's attention.
Edit intent: meaning-changed
Original:  Using these results, we show that a set (possibly a singleton) of strict preference orderings compatible with RAM is identifiable from the decision maker's choice probabilities, and establish a representation of this identified set of unobserved preferencesas a collection of inequality constrains on her choice probabilities.
Revised:  Based on these theoretical findings, we propose econometric methods for identification, estimation, and inference of the decision maker's choice probabilities, and establish a representation of this identified set of unobserved preferencesas a collection of inequality constrains on her choice probabilities.
Edit intent: meaning-changed
Original:  Using these results, we show that a set (possibly a singleton) of strict preference orderings compatible with RAM is identifiable from the decision maker's choice probabilities, and establish a representation of this identified set of unobserved preferencesas a collection of inequality constrains on her choice probabilities. Given this nonparametric identification result, we develop uniformly valid inference methods for the (partially) identifiable preferences. We showcase the performance of our proposed econometric methods using simulations, and provide general-purpose software implementation of our estimation and inference results in theR software package\texttt{ramchoice .
Revised:  Using these results, we show that a set (possibly a singleton) of strict preference orderings compatible with RAM is identifiable from the decision maker's preferences. To illustrate the applicability of our results and their concrete empirical content in specific settings, we also develop revealed preference theory and accompanying econometric methods under additional nonparametric assumptions on the consideration set for binary choice problems. Finally, we provide general purpose software implementation of our estimation and inference results in theR software package\texttt{ramchoice .
Edit intent: clarity
Original:  We showcase the performance of our proposed econometric methods using simulations, and provide general-purpose software implementation of our estimation and inference results in theR software package\texttt{ramchoice . Our proposed econometric methods are computationally very fast to implement .
Revised:  We showcase the performance of our proposed econometric methods using simulations, and provide general-purpose software implementation of our estimation and inference results in theR software package\texttt{ramchoice , and showcase their performance using simulations .
Edit intent: meaning-changed
Original: In this paper we study the following problem: we are given a set of imprecise points modeled as parallel line segments  , and we wish to place a point on each line segment such that the resulting point set maximizes /minimizes the size of the largest /smallest area k-gon.
Revised: Assume we are given a set of imprecise points modeled as parallel line segments , and we wish to place a point on each line segment such that the resulting point set maximizes /minimizes the size of the largest /smallest area k-gon.
Edit intent: clarity
Original: In this paper we study the following problem: we are given a set of imprecise points modeled as parallel line segments  , and we wish to place a point on each line segment such that the resulting point set maximizes /minimizes the size of the largest /smallest area k-gon.
Revised: In this paper we study the following problem: we are given a set of parallel line segments , and we wish to place a point on each line segment such that the resulting point set maximizes /minimizes the size of the largest /smallest area k-gon.
Edit intent: clarity
Original: In this paper we study the following problem: we are given a set of imprecise points modeled as parallel line segments  , and we wish to place a point on each line segment such that the resulting point set maximizes /minimizes the size of the largest /smallest area k-gon.
Revised: In this paper we study the following problem: we are given a set of imprecise points modeled as parallel line segments in the plane , and we wish to place a point on each line segment such that the resulting point set maximizes /minimizes the size of the largest /smallest area k-gon.
Edit intent: meaning-changed
Original: In this paper we study the following problem: we are given a set of imprecise points modeled as parallel line segments  , and we wish to place a point on each line segment such that the resulting point set maximizes /minimizes the size of the largest /smallest area k-gon.
Revised: In this paper we study the following problem: we are given a set of imprecise points modeled as parallel line segments , and we wish to place a point on each line segment such that the resulting point set maximizes or minimizes the area of the largest /smallest area k-gon.
Edit intent: fluency
Original: In this paper we study the following problem: we are given a set of imprecise points modeled as parallel line segments  , and we wish to place a point on each line segment such that the resulting point set maximizes /minimizes the size of the largest /smallest area k-gon. We first study the problem for the case k=3. We show that for a given set of parallel line segments of equal length the largest possible area triangle can be found in O(n \log n) time , and for line segments of arbitrary length the problem can be solved in O(n ^2) time .
Revised: In this paper we study the following problem: we are given a set of imprecise points modeled as parallel line segments , and we wish to place a point on each line segment such that the resulting point set maximizes /minimizes the size of the largest or smallest triangle in the set. We analyze the complexity of the four resulting computational problems, and we show that three of them admit polynomial-time algorithms, while the fourth is NP-hard. Specifically, we show that maximizing the largest triangle can be found in O(n \log n) time , and for line segments of arbitrary length the problem can be solved in O(n ^2) time .
Edit intent: meaning-changed
Original:  We show that for a given set of parallel line segments of equal length the largest possible area triangle can be found in O(n \log n) time , and for line segments of arbitrary length the problem can be solved in O(n ^2) time .
Revised:  We show that for a given set of parallel line segments of equal length the largest possible area triangle can be done in O(n \log n) time , and for line segments of arbitrary length the problem can be solved in O(n ^2) time .
Edit intent: clarity
Original:  We show that for a given set of parallel line segments of equal length the largest possible area triangle can be found in O(n \log n) time , and for line segments of arbitrary length the problem can be solved in O(n ^2) time .
Revised:  We show that for a given set of parallel line segments of equal length the largest possible area triangle can be found in O(n ^2) time (or in O(n ^2) time .
Edit intent: coherence
Original:  We show that for a given set of parallel line segments of equal length the largest possible area triangle can be found in O(n \log n) time , and for line segments of arbitrary length the problem can be solved in O(n ^2) time . Also, we show that the smallest largest-area triangle can be found in O(n^2 \log n) time .
Revised:  We show that for a given set of parallel line segments of equal length the largest possible area triangle can be found in O(n \log n) time , and for line segments of arbitrary length the problem can be solved in O(n \log n) time for unit segments); minimizing the largest triangle can be found in O(n^2 \log n) time .
Edit intent: meaning-changed
Original:  Also, we show that the smallest largest-area triangle can be found in O(n^2 \log n) time . As for finding smallest-area triangles, we show that finding the largest smallest-area triangle is NP-hard , but that the smallest possible area triangle for a set of arbitrary length parallel line segments can be found in O(n^2) time.
Revised:  Also, we show that the smallest largest-area triangle can be found in O(n^2 \log n) time ; maximizing the smallest triangle is NP-hard , but that the smallest possible area triangle for a set of arbitrary length parallel line segments can be found in O(n^2) time.
Edit intent: meaning-changed
Original:  As for finding smallest-area triangles, we show that finding the largest smallest-area triangle is NP-hard , but that the smallest possible area triangle for a set of arbitrary length parallel line segments can be found in O(n^2) time.
Revised:  As for finding smallest-area triangles, we show that finding the largest smallest-area triangle is NP-hard ; but minimizing the smallest triangle can be done in O(n^2) time.
Edit intent: clarity
Original:  The recent Leaky Integrate-and-Fire with Latency (LIFL) spiking neuron model is event-driven compatible and exhibits some realistic neuronal features, opening new horizons in whole-brain modelling.
Revised:  The recent Leaky Integrate-and-Fire with Latency (LIFL) spiking neuron model is event-driven compatible and exhibits some realistic neuronal features, opening new avenues for brain modelling.
Edit intent: clarity
Original:  In this paper we present FNS, a LIFL-based exact event-driven spiking neural network framework implemented in Java and oriented to wholebrain simulations. FNS combines spiking/synaptic whole-brain modelling with the event-driven approach, allowing us to define heterogeneous  modules and multi-scale connectivity with delayed connections and plastic synapses , providing fast simulations at the same time.
Revised:  In this paper we present FNS, a LIFL-based exact event-driven spiking neural network framework , which combines spiking/synaptic whole-brain modelling with the event-driven approach, allowing us to define heterogeneous modules and multi-scale connectivity with delayed connections and plastic synapses , providing fast simulations at the same time.
Edit intent: coherence
Original:  FNS combines spiking/synaptic whole-brain modelling with the event-driven approach, allowing us to define heterogeneous  modules and multi-scale connectivity with delayed connections and plastic synapses , providing fast simulations at the same time.
Revised:  FNS combines spiking/synaptic neural modelling with the event-driven approach, allowing us to define heterogeneous modules and multi-scale connectivity with delayed connections and plastic synapses , providing fast simulations at the same time.
Edit intent: clarity
Original:  FNS combines spiking/synaptic whole-brain modelling with the event-driven approach, allowing us to define heterogeneous  modules and multi-scale connectivity with delayed connections and plastic synapses , providing fast simulations at the same time.
Revised:  FNS combines spiking/synaptic whole-brain modelling with the event-driven approach, allowing us to define heterogeneous neuron modules and multi-scale connectivity with delayed connections and plastic synapses , providing fast simulations at the same time.
Edit intent: meaning-changed
Original:  FNS combines spiking/synaptic whole-brain modelling with the event-driven approach, allowing us to define heterogeneous  modules and multi-scale connectivity with delayed connections and plastic synapses , providing fast simulations at the same time. A novel parallelization strategy is also implemented in order to further speed up simulations .
Revised:  FNS combines spiking/synaptic whole-brain modelling with the event-driven approach, allowing us to define heterogeneous modules and multi-scale connectivity with delayed connections and plastic synapses . In order to allow multi-thread implementations a novel parallelization strategy is also implemented in order to further speed up simulations .
Edit intent: coherence
Original:  Finally, a reduced brain network model (1400 neurons and 45000 synapses) is synthesized on the basis of real brain structural data, and the resulting model activity is compared with associated brain functional (source-space MEG) data .
Revised:  Finally, a brain subnetwork is modeled on the basis of real brain structural data, and the resulting model activity is compared with associated brain functional (source-space MEG) data .
Edit intent: meaning-changed