wanyu/IteraTeR_v2 huggingface dataset:
Original:  , the "Collatz encoding" of a parity vector p, and the (0,-1)-tree, a binary tree which dictates the structure of first occurrence of parity vectors in the Collatz graph by using modular arithmetic in Z/}%DIFDELCMD < {%%% 3^k \mathbb{Z [ TCS 2011 , exploits the properties of first occurrence of parity vectors via their encoding \mathcal{E (p) and the symmetries of the (\alpha_{0,-1})-tree in order to highlight some regularstructure in the Collatz graph.
Revised:  , the "Collatz encoding" of a parity vector p, and the (0,-1)-tree, a binary tree which dictates the structure of first occurrence of parity vectors in the Collatz graph by using modular arithmetic in Z/}%DIFDELCMD < {%%% \mathbb{Z [ TCS 2011 , exploits the properties of first occurrence of parity vectors via their encoding \mathcal{E (p) and the symmetries of the (\alpha_{0,-1})-tree in order to highlight some regularstructure in the Collatz graph.
Edit intent: clarity
Original:  , the "Collatz encoding" of a parity vector p, and the (0,-1)-tree, a binary tree which dictates the structure of first occurrence of parity vectors in the Collatz graph by using modular arithmetic in Z/}%DIFDELCMD < {%%% 3^k \mathbb{Z [ TCS 2011 , exploits the properties of first occurrence of parity vectors via their encoding \mathcal{E (p) and the symmetries of the (\alpha_{0,-1})-tree in order to highlight some regularstructure in the Collatz graph.
Revised:  , the "Collatz encoding" of a parity vector p, and the (0,-1)-tree, a binary tree which dictates the structure of first occurrence of parity vectors in the Collatz graph by using modular arithmetic in Z/}%DIFDELCMD < {%%% 3^k \mathbb{Z [ , exploits the properties of first occurrence of parity vectors via their encoding \mathcal{E (p) and the symmetries of the (\alpha_{0,-1})-tree in order to highlight some regularstructure in the Collatz graph.
Edit intent: coherence
Original:  , the "Collatz encoding" of a parity vector p, and the (0,-1)-tree, a binary tree which dictates the structure of first occurrence of parity vectors in the Collatz graph by using modular arithmetic in Z/}%DIFDELCMD < {%%% 3^k \mathbb{Z [ TCS 2011 , exploits the properties of first occurrence of parity vectors via their encoding \mathcal{E (p) and the symmetries of the (\alpha_{0,-1})-tree in order to highlight some regularstructure in the Collatz graph.
Revised:  , the "Collatz encoding" of a parity vector p, and the (0,-1)-tree, a binary tree which dictates the structure of first occurrence of parity vectors in the Collatz graph by using modular arithmetic in Z/}%DIFDELCMD < {%%% 3^k \mathbb{Z [ TCS 2011 (p) and the symmetries of the (\alpha_{0,-1})-tree in order to highlight some regularstructure in the Collatz graph.
Edit intent: coherence
Original:  We show that the k-span predecessor set of x\in\mathbb{N} in }   the Collatz graph , which contains any ancestor y of x that uses exactly k times the map T_1 (and any number of times the map T_0) in order to reach x, can be defined, in binary, by a regular expression  \texttt{reg}_k(x) . Hence, we exhibit a general regular structure in the Collatz graph.
Revised:  We show that the k-span predecessor set of x\in\mathbb{N} in } the Collatz graph naturally leads to the construction of a regular expression \texttt{reg}_k(x) . Hence, we exhibit a general regular structure in the Collatz graph.
Edit intent: clarity
Original:  We show that the k-span predecessor set of x\in\mathbb{N} in }   the Collatz graph , which contains any ancestor y of x that uses exactly k times the map T_1 (and any number of times the map T_0) in order to reach x, can be defined, in binary, by a regular expression  \texttt{reg}_k(x) . Hence, we exhibit a general regular structure in the Collatz graph.
Revised:  We show that the k-span predecessor set of x\in\mathbb{N} in } the Collatz graph , which contains any ancestor y of x that uses exactly k times the map T_1 (and any number of times the map T_0) in order to reach x, can be defined, in binary, by a regular expression , \texttt{reg}_k(x) . Hence, we exhibit a general regular structure in the Collatz graph.
Edit intent: fluency
Original:  Based on that construction, we implement the algorithm which generates }\texttt{ [  .
Revised:  Based on that construction, we implement the algorithm which generates }\texttt{reg [ .
Edit intent: fluency
Original:  Based on that construction, we implement the algorithm which generatesreg _k(x) for any x and k.
Revised:  reg _k(x) for any x and k.
Edit intent: clarity
Original:  Based on that construction, we implement the algorithm which generatesreg _k(x) for any x and k.
Revised:  Based on that construction, we implement the algorithm which generates _k(x) for any x and k.
Edit intent: clarity
Original:  Our result generalises Colussi's work on the x = 1 case [TCS 2011] to any natural number x, and gives a new exploratory tool for further study of the Collatz graph in binary.
Revised:  Our result generalises Colussi's work on the x = 1 case [TCS 2011] to any natural number x, and gives mathematical and algorithmic tools for further exploration of the Collatz graph in binary.
Edit intent: clarity
Original: Distributed systems address an increasing demand for fast access to resources and provide fault tolerance for data.
Revised: Distributed systems address the increasing demand for fast access to resources and provide fault tolerance for data.
Edit intent: fluency
Original: Distributed systems address an increasing demand for fast access to resources and provide fault tolerance for data.
Revised: Distributed systems address an increasing demand for fast access to resources and fault tolerance for data.
Edit intent: clarity
Original:  In contrast, data flows from data with weak consistency to data with strong consistency requirements are problematic, since application correctness may be broken.
Revised:  In contrast, data flow from data with weak consistency to data with strong consistency requirements are problematic, since application correctness may be broken.
Edit intent: fluency
Original:  In contrast, data flows from data with weak consistency to data with strong consistency requirements are problematic, since application correctness may be broken.
Revised:  In contrast, data flows from data with weak consistency to data with strong consistency requirements is problematic, since application correctness may be broken.
Edit intent: fluency
Original:  There are two principal new features: first, the type system statically enforces noninterference between data types with weak consistency and data types with strong consistency ;
Revised:  The type system of LCD statically enforces noninterference between data types with weak consistency and data types with strong consistency ;
Edit intent: clarity
Original:  The type system of LCD statically enforces noninterference between data types with weak consistency and data types with strong consistency.
Revised:  The type system of LCD statically enforces noninterference between data types with weaker consistency and data types with strong consistency.
Edit intent: fluency
Original:  The language can be applied to many distributed applications and guarantees that the updates of weakly-consistent data can never affect strongly-consistent data.
Revised:  The language can be applied to many distributed applications and guarantees that updates of weakly-consistent data can never affect strongly-consistent data.
Edit intent: fluency
Original:  We also extend the basic CTRD with an optimization that reduces synchronization times for generating reference graphs.
Revised:  We also extend the basic CTRD with an optimization that reduces synchronization for generating reference graphs.
Edit intent: clarity
Original:  It operates  in generic scenes and is robust to difficult occlusions both by other people and objects .
Revised:  It operates successfully in generic scenes and is robust to difficult occlusions both by other people and objects .
Edit intent: clarity
Original:  It operates  in generic scenes and is robust to difficult occlusions both by other people and objects .
Revised:  It operates in generic scenes which may contain occlusions by objects and by other people .
Edit intent: clarity
Original:  In the second stage, a fully-connected neural network turns the possibly partial (on account of occlusion) 2D pose and 3D pose features for each subject into a complete 3D pose estimate per individual.
Revised:  In the second stage, a fully connected neural network turns the possibly partial (on account of occlusion) 2D pose and 3D pose features for each subject into a complete 3D pose estimate per individual.
Edit intent: fluency
Original:  In the second stage, a fully-connected neural network turns the possibly partial (on account of occlusion) 2D pose and 3D pose features for each subject into a complete 3D pose estimate per individual.
Revised:  In the second stage, a fully-connected neural network turns the possibly partial (on account of occlusion) 2Dpose and 3Dpose features for each subject into a complete 3D pose estimate per individual.
Edit intent: fluency
Original:  In the second stage, a fully-connected neural network turns the possibly partial (on account of occlusion) 2D pose and 3D pose features for each subject into a complete 3D pose estimate per individual.
Revised:  In the second stage, a fully-connected neural network turns the possibly partial (on account of occlusion) 2D pose and 3D pose features for each subject into a complete 3Dpose estimate per individual.
Edit intent: fluency
Original:  This is a further key distinction from previous work that neither extracted global body positions nor joint angle results of a coherent skeleton in real time for multi-person scenes.
Revised:  This is a further key distinction from previous work that do not produce joint angle results of a coherent skeleton in real time for multi-person scenes.
Edit intent: clarity
Original:  Finally, we discuss how the "small-world" property affects the performance of graph-based approaches .
Revised:  Finally, we discuss how the "small-world" property affects the performance of graph-based NNS algorithms .
Edit intent: clarity
Original:  We fill this gap and rigorously analyze the performance of graph-based NNS algorithms, specifically focusing on the low-dimensional (d << \log (n) ) regime.
Revised:  We fill this gap and rigorously analyze the performance of graph-based NNS algorithms, specifically focusing on the low-dimensional (d << \log n ) regime.
Edit intent: fluency
Original: Climatic response of population boundaries, known as ecotone, is a classic indicator  in ecology.
Revised: Population boundary is a classic indicator in ecology.
Edit intent: clarity
Original: Climatic response of population boundaries, known as ecotone, is a classic indicator  in ecology.
Revised: Climatic response of population boundaries, known as ecotone, is a classic indicator of climatic response in ecology.
Edit intent: clarity
Original:  Here, we capture the effects of time-independent, quenched spatial heterogeneities on the ecological boundary with the disordered contact process in one and two dimensions with a linear spatial trend in the local control parameter.
Revised:  Here, we capture the effects of quenched heterogeneities on the ecological boundary with the disordered contact process in one and two dimensions with a linear spatial trend in the local control parameter.
Edit intent: clarity
Original:  This system, called Katecheo, includes four configurable modules that collectively enable identification of questions, classification of those questions into topics, a searchof knowledge base articles , and reading comprehension.
Revised:  This system, called Katecheo, includes four configurable modules that collectively enable identification of questions, classification of those questions into topics, document search , and reading comprehension.
Edit intent: clarity
Original:  We demonstrate the system using publicly available , pre-trained models and knowledge base articles extracted from Stack Exchange sites.
Revised:  We demonstrate the system using publicly available knowledge base articles extracted from Stack Exchange sites.
Edit intent: clarity
Original:  The geometry is discretized in uniform 2D or 3D lattices by locating the curved cylindrical boundaries halfway between lattice nodes.
Edit intent: coherence
Original: We report the first implementation of the lattice Boltzmann method (LBM) to integrate the Bloch-Torrey equation, which describes the evolution of the transverse magnetization vector and the fate of the signal of diffusion magnetic resonance imaging (dMRI).
Revised: We report an implementation of the lattice Boltzmann method (LBM) to integrate the Bloch-Torrey equation, which describes the evolution of the transverse magnetization vector and the fate of the signal of diffusion magnetic resonance imaging (dMRI).
Edit intent: clarity
Original:  Motivated by the need to interpret dMRI experiments in biological tissues, and to offset the small time step limitation of classical LBM, a hybrid LBM scheme is introduced and implemented to solve the Bloch-Torrey equation.
Revised:  Motivated by the need to interpret dMRI experiments in biological tissues, and to offset the small time-step limitation of classical LBM, a hybrid LBM scheme is introduced and implemented to solve the Bloch-Torrey equation.
Edit intent: fluency
Original:  Moreover, by exploiting the structure of the NEP we present algorithm specializations for NEP methods, although the technique also allows general solution methods for NEPs to be directly applied to the problem .
Revised:  Moreover, by exploiting the structure of the NEP we present algorithm specializations for NEP methods, although the technique also allows general solution methods for NEPs to be directly applied .
Edit intent: clarity
Original:  The nonlinearization is illustrated in examples and simulations, with focus on problems where the eliminated equation is of much smaller dimensions than the other two-parameter eigenvalue equation , in particular applications in domain decomposition .
Revised:  The nonlinearization is illustrated in examples and simulations, with focus on problems where the eliminated equation is of much smaller size than the other two-parameter eigenvalue equation , in particular applications in domain decomposition .
Edit intent: clarity
Original:  The nonlinearization is illustrated in examples and simulations, with focus on problems where the eliminated equation is of much smaller dimensions than the other two-parameter eigenvalue equation , in particular applications in domain decomposition .
Revised:  The nonlinearization is illustrated in examples and simulations, with focus on problems where the eliminated equation is of much smaller dimensions than the other two-parameter eigenvalue equation . This situation arises naturally in domain decomposition techniques .
Edit intent: coherence
Original:  A general  analysis is also carried out under the assumption that a backward stable eigenvalue solver method is used to solve the eliminated problem, leading to the conclusion that the error is benign  .
Revised:  A general error analysis is also carried out under the assumption that a backward stable eigenvalue solver method is used to solve the eliminated problem, leading to the conclusion that the error is benign .
Edit intent: clarity
Original:  A general  analysis is also carried out under the assumption that a backward stable eigenvalue solver method is used to solve the eliminated problem, leading to the conclusion that the error is benign  .
Revised:  A general analysis is also carried out under the assumption that a backward stable eigenvalue solver method is used to solve the eliminated problem, leading to the conclusion that the error is benign in this situation .
Edit intent: clarity
Original:  The local rule is only based on the presence of neighbouring agents, and whether a neighbour marks the agent's current location.
Revised:  The local rule is based only on the presence of neighbouring agents, and whether a neighbour marks the agent's current location.
Edit intent: fluency
Original:  The local rule is only based on the presence of neighbouring agents, and whether a neighbour marks the agent's current location.
Revised:  The local rule is only based on the presence of neighbouring robots, and on whether a settled robot points to the current location.
Edit intent: clarity
Original:  Our goal is to show that even under conditions of asynchronicity, frequent crashing, and limited physical space, the simple mobile agents successfully cover the environment and construct a distributed spanning tree in linear time . Specifically, we show that, assuming at most ct/4 crashes happen before time t for all times t, the agents can complete the tree asymptotically almost surely in 8%DIFDELCMD < \big(%%% (1-c)^{-1+o(1)}%DIFDELCMD < \big)%%% n time where n is the number of vertices.
Revised:  Our goal is to show that even under conditions of asynchronicity, frequent crashing, and limited physical space, the simple mobile robots complete their mission in linear time . Specifically, we show that, assuming at most ct/4 crashes happen before time t for all times t, the agents can complete the tree asymptotically almost surely in 8%DIFDELCMD < \big(%%% (1-c)^{-1+o(1)}%DIFDELCMD < \big)%%% n time where n is the number of vertices.
Edit intent: clarity
Original:  Our goal is to show that even under conditions of asynchronicity, frequent crashing, and limited physical space, the simple mobile agents successfully cover the environment and construct a distributed spanning tree in linear time . Specifically, we show that, assuming at most ct/4 crashes happen before time t for all times t, the agents can complete the tree asymptotically almost surely in 8%DIFDELCMD < \big(%%% (1-c)^{-1+o(1)}%DIFDELCMD < \big)%%% n time where n is the number of vertices.
Revised:  Our goal is to show that even under conditions of asynchronicity, frequent crashing, and limited physical space, the simple mobile agents successfully cover the environment and construct a distributed spanning tree in linear time asymptotically almost surely in 8%DIFDELCMD < \big(%%% (1-c)^{-1+o(1)}%DIFDELCMD < \big)%%% n time where n is the number of vertices.
Edit intent: coherence
Original:  Our goal is to show that even under conditions of asynchronicity, frequent crashing, and limited physical space, the simple mobile agents successfully cover the environment and construct a distributed spanning tree in linear time . Specifically, we show that, assuming at most ct/4 crashes happen before time t for all times t, the agents can complete the tree asymptotically almost surely in 8%DIFDELCMD < \big(%%% (1-c)^{-1+o(1)}%DIFDELCMD < \big)%%% n time where n is the number of vertices.
Revised:  Our goal is to show that even under conditions of asynchronicity, frequent crashing, and limited physical space, the simple mobile agents successfully cover the environment and construct a distributed spanning tree in linear time . Specifically, we show that, assuming at most ct/4 crashes happen before time t for all times t, the agents can complete the tree asymptotically almost surely %DIFDELCMD < \big(%%% (1-c)^{-1+o(1)}%DIFDELCMD < \big)%%% n time where n is the number of vertices.
Edit intent: clarity
Original:  The analysis relates our algorithm to the `` totally asymmetric simple exclusion process '' in statistical mechanics.
Revised:  The analysis relates our algorithm to the `` totally asymmetric simple exclusion process " in statistical mechanics.
Edit intent: fluency
Original:  They grow the environment's coverage by ` settling' at empty locations and aiding other robots' navigation from these locations.
Revised:  They grow the environment's coverage by ' settling' at empty locations and aiding other robots' navigation from these locations.
Edit intent: fluency
Original:  Here, we experimentally demonstrate one of such devices, skyrmion-based artificial synaptic device designed for neuromorphic computing.
Revised:  Here, we experimentally demonstrate such a device: electrically-operating skyrmion-based artificial synaptic device designed for neuromorphic computing.
Edit intent: clarity
Original:  Moreover , we demonstrate that such skyrmion-based synapses can be used to perform neuromorphic pattern-recognition computing using handwritten recognition data set, reaching to the accuracy of ~89 percents, comparable to the software-based training accuracy of ~ 93 percents.
Revised:  Moreover , we demonstrate that such skyrmion-based synapses could be used to perform neuromorphic pattern-recognition computing using handwritten recognition data set, reaching to the accuracy of ~89 percents, comparable to the software-based training accuracy of ~ 93 percents.
Edit intent: fluency
Original: In this work , we introduce three generic point cloud processing blocks that improve both accuracy and memory consumption of state-of-the-art networks thus allowing to design deeper and more accurate networks.
Revised: In this work we introduce Lean Point Networks (LPNs) to train deeper and more accurate networks.
Edit intent: clarity
Original:  a convolution-type operation for point sets that blends neighborhood information in a memory-efficient manner;
Revised:  a convolution-type block for point sets that blends neighborhood information in a memory-efficient manner;
Edit intent: clarity
Original:  and a crosslink block that efficiently shares information across low- and high-resolution processing branches . Combining these blocksallows us to design significantly wider and deeper  architectures.
Revised:  a crosslink block that efficiently shares information across low- and high-resolution processing branches . Combining these blocksallows us to design significantly wider and deeper architectures.
Edit intent: coherence
Original:  We extensively evaluate the proposed architectures on multiple point segmentation benchmarks (ShapeNet-Part, ScanNet, PartNet) and report systematic improvements in terms of both accuracy and memory consumption  by using our generic modules in conjunction with multiple recent architectures (PointNet++, DGCNN, SpiderCNN , PointCNN) .
Revised:  We report systematic accuracy and memory consumption by using our generic modules in conjunction with multiple recent architectures (PointNet++, DGCNN, SpiderCNN , PointCNN) .
Edit intent: coherence
Original:  We extensively evaluate the proposed architectures on multiple point segmentation benchmarks (ShapeNet-Part, ScanNet, PartNet) and report systematic improvements in terms of both accuracy and memory consumption  by using our generic modules in conjunction with multiple recent architectures (PointNet++, DGCNN, SpiderCNN , PointCNN) .
Revised:  We extensively evaluate the proposed architectures on multiple point segmentation benchmarks (ShapeNet-Part, ScanNet, PartNet) and report systematic improvements in terms of both accuracy and memory consumption by using our generic modules as drop-in replacements for the blocks of multiple architectures (PointNet++, DGCNN, SpiderCNN , PointCNN) .
Edit intent: clarity
Original:  We extensively evaluate the proposed architectures on multiple point segmentation benchmarks (ShapeNet-Part, ScanNet, PartNet) and report systematic improvements in terms of both accuracy and memory consumption  by using our generic modules in conjunction with multiple recent architectures (PointNet++, DGCNN, SpiderCNN , PointCNN) .
Revised:  We extensively evaluate the proposed architectures on multiple point segmentation benchmarks (ShapeNet-Part, ScanNet, PartNet) and report systematic improvements in terms of both accuracy and memory consumption by using our generic modules in conjunction with multiple recent architectures (PointNet++, DGCNN, SpiderNet , PointCNN) .
Edit intent: fluency