wanyu/IteraTeR_v2 huggingface dataset:
Original:  In this work, we propose a novel methodology to measure the topological resilience and robustness of a network based on Information Theory quantifiers.
Revised:  In this work, we propose a novel methodology to measure the structural robustness of a network based on Information Theory quantifiers.
Edit intent: clarity
Original:  Although both cases show to be able to detect any single topological change, the distance distribution seems to be more consistent to reflect the network structural deviations.
Revised:  Although both cases show to be able to detect any single topological change, the distance distribution seems to be more consistent in capturing network structural deviations.
Edit intent: clarity
Original:  In all cases, the novel resilience and robustness measures computed by using the distance distribution reflect better the consequences of the failures , outperforming other methods .
Revised:  In all cases, the novel robustness measure computed by using the distance distribution reflect better the consequences of the failures , outperforming other methods .
Edit intent: clarity
Original:  In all cases, the novel resilience and robustness measures computed by using the distance distribution reflect better the consequences of the failures , outperforming other methods .
Revised:  In all cases, the novel resilience and robustness measures computed by using the distance distribution better reflect the consequences of the failures , outperforming other methods .
Edit intent: fluency
Original:  In all cases, the novel resilience and robustness measures computed by using the distance distribution reflect better the consequences of the failures , outperforming other methods .
Revised:  In all cases, the novel resilience and robustness measures computed by using the distance distribution reflect better the consequences of the failures .
Edit intent: clarity
Original: A crucial challenge in network theory is to study how robust a network is when facing failures or attacks .
Revised: A crucial challenge in network theory is the study of the robustness of a network after facing a sequence of failures .
Edit intent: clarity
Original:  In this work, we propose a novel methodology to measure the structural robustness of a network based on Information Theory quantifiers.
Revised:  In this work, we propose a dynamical definition of network's robustness based on Information Theory quantifiers.
Edit intent: clarity
Original:  In particular, we analyze the efficiency  in capturing small perturbations in the network's topology when using the degree and distance distributions.
Revised:  In particular, we analyze the efficiency of the method in capturing small perturbations in the network's topology when using the degree and distance distributions.
Edit intent: clarity
Original:  In particular, we analyze the efficiency  in capturing small perturbations in the network's topology when using the degree and distance distributions.
Revised:  In particular, we analyze the efficiency in capturing small perturbations by considering both, the degree and distance distributions.
Edit intent: clarity
Original:  Additionally , the pace of the expected changes is likely to be abrupt: catastrophic shifts might be the most likely outcome of this ongoing, apparently slow process.
Revised:  Furthermore , the pace of the expected changes is likely to be abrupt: catastrophic shifts might be the most likely outcome of this ongoing, apparently slow process.
Edit intent: fluency
Original:  The question is whether there exists a set S of at most k vertices such that every vertex v\in V\setminus S has at least \phi(v) vertex-disjoint paths to S  . The problem is NP-hard \NP already for instances with d=4 (Cicalese et al., manuscript '14), admits a log-factor approximation (Boros et al., Networks '14), and is fixed-parameter tractable in terms of  k (Lokshtanov, private communication '14).
Revised:  The question is whether there exists a set S of at most k vertices such that every vertex v\in V\setminus S has at least \phi(v) vertex-disjoint paths to S . The problem is \NP already for instances with d=4 (Cicalese et al., manuscript '14), admits a log-factor approximation (Boros et al., Networks '14), and is fixed-parameter tractable in terms of k (Lokshtanov, private communication '14).
Edit intent: clarity
Original:  The question is whether there exists a set S of at most k vertices such that every vertex v\in V\setminus S has at least \phi(v) vertex-disjoint paths to S  . The problem is NP-hard \NP already for instances with d=4 (Cicalese et al., manuscript '14), admits a log-factor approximation (Boros et al., Networks '14), and is fixed-parameter tractable in terms of  k (Lokshtanov, private communication '14).
Revised:  The question is whether there exists a set S of at most k vertices such that every vertex v\in V\setminus S has at least \phi(v) vertex-disjoint paths to S . The problem is NP-hard \NP-hard already for instances with d=4 (Cicalese et al., manuscript '14), admits a log-factor approximation (Boros et al., Networks '14), and is fixed-parameter tractable in terms of k (Lokshtanov, private communication '14).
Edit intent: clarity
Original:  The question is whether there exists a set S of at most k vertices such that every vertex v\in V\setminus S has at least \phi(v) vertex-disjoint paths to S  . The problem is NP-hard \NP already for instances with d=4 (Cicalese et al., manuscript '14), admits a log-factor approximation (Boros et al., Networks '14), and is fixed-parameter tractable in terms of  k (Lokshtanov, private communication '14).
Revised:  The question is whether there exists a set S of at most k vertices such that every vertex v\in V\setminus S has at least \phi(v) vertex-disjoint paths to S . The problem is NP-hard \NP already for instances with d=4 (Cicalese et al., manuscript '14), admits a log-factor approximation (Boros et al., Networks '14), and is fixed-parameter tractable in terms of k (Lokshtanov, unpublished '14).
Edit intent: clarity
Original: In massive MIMO systems, the matched filter (MF) beamformer is attractive due to its extremely low complexity of implementation compared to those high-complexity decomposition-based beamformers like zero-forcing, block diagonalization, maximum signal-leakage-and-noise ratio, and minimum mean square error.
Revised: In massive MIMO systems, the matched filter (MF) beamforming is attractive technique due to its extremely low complexity of implementation compared to those high-complexity decomposition-based beamformers like zero-forcing, block diagonalization, maximum signal-leakage-and-noise ratio, and minimum mean square error.
Edit intent: clarity
Original: In massive MIMO systems, the matched filter (MF) beamformer is attractive due to its extremely low complexity of implementation compared to those high-complexity decomposition-based beamformers like zero-forcing, block diagonalization, maximum signal-leakage-and-noise ratio, and minimum mean square error.
Revised: In massive MIMO systems, the matched filter (MF) beamformer is attractive due to its extremely low complexity of implementation compared to those high-complexity decomposition-based beamforming techniques such as zero-forcing, block diagonalization, maximum signal-leakage-and-noise ratio, and minimum mean square error.
Edit intent: clarity
Original:  This paper derives an approximate formula for probability density function (PDF) of received signal-to-interference-and-noise ratio (SINR) at user terminal when MF is adopted at base station.
Revised:  This paper derives an approximate formula for probability density function (PDF) of the signal-to-interference-and-noise ratio (SINR) at user terminal when MF is adopted at base station.
Edit intent: clarity
Original:  This distribution of SINR can be used to make an analysis of average sum-rate, outage probability, and symbol error rate of massive MIMO downlink with MF at BS.
Revised:  This distribution of SINR can be used to calculate the symbol error rate of massive MIMO downlink with MF at BS.
Edit intent: clarity
Original:  From simulation , we find that the derived approximate analytical expression for PDF of SINR is consistent with the simulated exact PDF from the definition of SINR in medium-scale and large-scale MIMO systems.
Revised:  From simulation , we find that the derived approximate analytical expression for PDF is consistent with the simulated exact PDF from the definition of SINR in medium-scale and large-scale MIMO systems.
Edit intent: clarity
Original:  From simulation , we find that the derived approximate analytical expression for PDF of SINR is consistent with the simulated exact PDF from the definition of SINR in medium-scale and large-scale MIMO systems.
Revised:  From simulation , we find that the derived approximate analytical expression for PDF of SINR is consistent with the simulated PDF in medium-scale and large-scale MIMO systems.
Edit intent: clarity
Original: In massive MIMO systems, the matched filter (MF) beamforming is attractive technique due to its extremely low complexity of implementation compared to those high-complexity decomposition-based beamforming techniques such as zero-forcing, block diagonalization, maximum signal-leakage-and-noise ratio, and minimum mean square error.
Revised: In massive MIMO systems, the matched filter (MF) beamforming is attractive technique due to its extremely low complexity of implementation compared to those high-complexity decomposition-based beamforming techniques such as zero-forcing, block diagonalization, and minimum mean square error.
Edit intent: clarity
Original: In massive MIMO systems, the matched filter (MF) beamforming is attractive technique due to its extremely low complexity of implementation compared to those high-complexity decomposition-based beamforming techniques such as zero-forcing, block diagonalization, and minimum mean square error.
Revised: In massive MIMO systems, the matched filter (MF) beamforming is attractive technique due to its extremely low complexity of implementation compared to those high-complexity decomposition-based beamforming techniques such as zero-forcing, and minimum mean square error.
Edit intent: clarity
Original:  It is confirmed by simulation that the derived approximate analytical expression for PDF is consistent with the simulated PDF in medium-scale and large-scale MIMO systems.
Revised:  It is confirmed by simulation that the derived approximate expression for PDF is consistent with the simulated PDF in medium-scale and large-scale MIMO systems.
Edit intent: clarity
Original:  In particular, we provide the connection between G and the groups generated by the orbit automata and use this connection to find elements of infinite order in certain automaton groups for which other methods failed to work .
Revised:  The connection between G and the groups generated by the orbit automata and use this connection to find elements of infinite order in certain automaton groups for which other methods failed to work .
Edit intent: coherence
Original:  In particular, we provide the connection between G and the groups generated by the orbit automata and use this connection to find elements of infinite order in certain automaton groups for which other methods failed to work .
Revised:  In particular, we provide the connection between G and the groups generated by the orbit automata is used to find elements of infinite order in certain automaton groups for which other methods failed to work .
Edit intent: clarity
Original:  Here I show that all these claims are wrong by astronomical factors.
Revised:  Here I show that all these statements are wrong by astronomical factors.
Edit intent: clarity
Original:  A reanalysis of the authors' experiments shows they are  consistent with humans discriminating just 10 odors.
Revised:  A reanalysis of the authors' experiments shows they are also consistent with humans discriminating just 10 odors.
Edit intent: clarity
Original:  We consider uncertainty under the existential model where each point's location is fixed but only occurs with a certain probability, and the locational model where each point has a probability distribution describing its location.
Revised:  We consider uncertainty in the existential model where each point's location is fixed but only occurs with a certain probability, and the locational model where each point has a probability distribution describing its location.
Edit intent: clarity
Original:  We consider approximating the expected width (an \epsilon-exp-kernel \expkernel ), as well as the probability distribution on the width (an \emph{%DIFDELCMD < \eps%%% -quant-kernel \probkernel ) for any direction.
Revised:  We consider approximating the expected width (an \expkernel ), as well as the probability distribution on the width (an \emph{%DIFDELCMD < \eps%%% -quant-kernel \probkernel ) for any direction.
Edit intent: clarity
Original:  We consider approximating the expected width (an \epsilon-exp-kernel \expkernel ), as well as the probability distribution on the width (an \emph{%DIFDELCMD < \eps%%% -quant-kernel \probkernel ) for any direction.
Revised:  We consider approximating the expected width (an \epsilon-exp-kernel \expkernel ), as well as the probability distribution on the width (an \emph{%DIFDELCMD < \eps%%% \probkernel ) for any direction.
Edit intent: clarity
Original: In this paper , given a parameter k, we demonstrate an infinite class of CNFs of treewidth at most k of their primary graphs such that the equivalent acyclic (syntactic) read-once switching and rectifier networks (AROSRNs) are of size at least n^{ck{\sc  {\sc   out the possibility of fixed-parameter space complexity of AROSRNs parameterized by the smallest treewidth of the equivalent CNF.
Revised: In this paper , given a parameter k, we demonstrate an infinite class of CNFs of treewidth at most k of their primary graphs such that the equivalent acyclic (syntactic) read-once branching programs ({\sc {\sc out the possibility of fixed-parameter space complexity of AROSRNs parameterized by the smallest treewidth of the equivalent CNF.
Edit intent: clarity
Original: KR2014%DIFDELCMD < ]%%% . We use the above lower bound {\sc  {\sc   to obtain a quasi-polynomial separation between Free Binary Decision Diagrams and Decision Decomposable Negation Normal Forms, essentially matching the simulation result of Beame ,Li,Roy,Suciu;UAI2013 and thus proving the tightness of the latter . Remark: This is a revised and extended version of the paper to appear in the proceedings of IPEC2014.
Revised: KR2014%DIFDELCMD < ]%%% {\sc {\sc to obtain a quasi-polynomial separation between Free Binary Decision Diagrams and Decision Decomposable Negation Normal Forms, essentially matching the simulation result of Beame ,Li,Roy,Suciu;UAI2013 and thus proving the tightness of the latter . Remark: This is a revised and extended version of the paper to appear in the proceedings of IPEC2014.
Edit intent: coherence
Original: KR2014%DIFDELCMD < ]%%% . We use the above lower bound {\sc  {\sc   to obtain a quasi-polynomial separation between Free Binary Decision Diagrams and Decision Decomposable Negation Normal Forms, essentially matching the simulation result of Beame ,Li,Roy,Suciu;UAI2013 and thus proving the tightness of the latter . Remark: This is a revised and extended version of the paper to appear in the proceedings of IPEC2014.
Revised: KR2014%DIFDELCMD < ]%%% . We use the above lower bound {\sc {\sc s to obtain a quasi-polynomial separation between Free Binary Decision Diagrams and Decision Decomposable Negation Normal Forms, essentially matching the simulation result of Beame ,Li,Roy,Suciu;UAI2013 and thus proving the tightness of the latter . Remark: This is a revised and extended version of the paper to appear in the proceedings of IPEC2014.
Edit intent: fluency
Original: KR2014%DIFDELCMD < ]%%% . We use the above lower bound {\sc  {\sc   to obtain a quasi-polynomial separation between Free Binary Decision Diagrams and Decision Decomposable Negation Normal Forms, essentially matching the simulation result of Beame ,Li,Roy,Suciu;UAI2013 and thus proving the tightness of the latter . Remark: This is a revised and extended version of the paper to appear in the proceedings of IPEC2014.
Revised: KR2014%DIFDELCMD < ]%%% . We use the above lower bound {\sc {\sc to obtain a quasi-polynomial separation between Free Binary Decision Diagrams and Decision Decomposable Negation Normal Forms, essentially matching the Beame ,Li,Roy,Suciu;UAI2013 and thus proving the tightness of the latter . Remark: This is a revised and extended version of the paper to appear in the proceedings of IPEC2014.
Edit intent: clarity
Original: KR2014%DIFDELCMD < ]%%% . We use the above lower bound {\sc  {\sc   to obtain a quasi-polynomial separation between Free Binary Decision Diagrams and Decision Decomposable Negation Normal Forms, essentially matching the simulation result of Beame ,Li,Roy,Suciu;UAI2013 and thus proving the tightness of the latter . Remark: This is a revised and extended version of the paper to appear in the proceedings of IPEC2014.
Revised: KR2014%DIFDELCMD < ]%%% . We use the above lower bound {\sc {\sc to obtain a quasi-polynomial separation between Free Binary Decision Diagrams and Decision Decomposable Negation Normal Forms, essentially matching the simulation result of existing upper bound introduced by Beame et al. and thus proving the tightness of the latter . Remark: This is a revised and extended version of the paper to appear in the proceedings of IPEC2014.
Edit intent: clarity
Original:  We reported an earlier version of proof of the parameterized lower bound in arXiv:1407.0491%DIFDELCMD < ]%%% . The present proof, although follows the same strategy, is implemented in a different way which we believe to be much simpler and more compact and readable .
Revised:  We reported an earlier version of proof of the parameterized lower bound in %DIFDELCMD < ]%%% . The present proof, although follows the same strategy, is implemented in a different way which we believe to be much simpler and more compact and readable .
Edit intent: coherence
Original:  We reported an earlier version of proof of the parameterized lower bound in arXiv:1407.0491%DIFDELCMD < ]%%% . The present proof, although follows the same strategy, is implemented in a different way which we believe to be much simpler and more compact and readable .
Revised:  We reported an earlier version of proof of the parameterized lower bound in arXiv:1407.0491%DIFDELCMD < ]%%% .
Edit intent: coherence
Original:  This paper introduces lazy basic block versioning, a simple JIT compilation architecture which effectively removes redundant type checks from critical code paths.
Revised:  This paper introduces lazy basic block versioning, a simple JIT compilation technique which effectively removes redundant type checks from critical code paths.
Edit intent: clarity
Original:  Our approach lazily generates type-specialized versions of basic blocks on-the-fly while propagating context-dependent type information.
Revised:  This novel approach lazily generates type-specialized versions of basic blocks on-the-fly while propagating context-dependent type information.
Edit intent: clarity
Original:  The combination of implementation simplicity, low algorithmic complexity and good run time performance makes basic block versioning attractive for baseline JIT compilers , eliminating the need for an interpreter .
Revised:  The combination of implementation simplicity, low algorithmic complexity and good run time performance makes basic block versioning attractive for baseline JIT compilers .
Edit intent: clarity
Original:  In particular, we summarize different characterisations of Forward AD, like the vector-matrix based approach, the idea of lifting functions to the algebra of dual numbers, the method of Taylor series expansion on dual numbers and the application of the push-forward operator .
Revised:  In particular, we explain why different characterisations of Forward AD, like the vector-matrix based approach, the idea of lifting functions to the algebra of dual numbers, the method of Taylor series expansion on dual numbers and the application of the push-forward operator .
Edit intent: clarity
Original:  Finally, we give a short summary of Reverse AD and again point out the underlying computational steps.
Revised:  We further give a short summary of Reverse AD and again point out the underlying computational steps.
Edit intent: clarity
Original: This article provides a short overview of the theory of First Order Automatic Differentiation (AD) for readers unfamiliar with this topic .
Revised: This article provides a short overview of the theory of First Order Automatic Differentiation (AD) .
Edit intent: clarity
Original:  In particular, we explain why different characterisations of Forward AD, like the vector-matrix based approach, the idea of lifting functions to the algebra of dual numbers, the method of Taylor series expansion on dual numbers and the application of the push-forward operator,  all reduce to the same actual chain of computations (and are, hence, equivalent) .
Revised:  In particular, we summarise different descriptions of the Forward Mode of AD, like the vector-matrix based approach, the idea of lifting functions to the algebra of dual numbers, the method of Taylor series expansion on dual numbers and the application of the push-forward operator, all reduce to the same actual chain of computations (and are, hence, equivalent) .
Edit intent: clarity
Original:  In particular, we explain why different characterisations of Forward AD, like the vector-matrix based approach, the idea of lifting functions to the algebra of dual numbers, the method of Taylor series expansion on dual numbers and the application of the push-forward operator,  all reduce to the same actual chain of computations (and are, hence, equivalent) .
Revised:  In particular, we explain why different characterisations of Forward AD, like the vector-matrix based approach, the idea of lifting functions to the algebra of dual numbers, the method of Taylor series expansion on dual numbers and the application of the push-forward operator, and explain why they all reduce to the same actual chain of computations (and are, hence, equivalent) .
Edit intent: coherence
Original:  In particular, we explain why different characterisations of Forward AD, like the vector-matrix based approach, the idea of lifting functions to the algebra of dual numbers, the method of Taylor series expansion on dual numbers and the application of the push-forward operator,  all reduce to the same actual chain of computations (and are, hence, equivalent) .
Revised:  In particular, we explain why different characterisations of Forward AD, like the vector-matrix based approach, the idea of lifting functions to the algebra of dual numbers, the method of Taylor series expansion on dual numbers and the application of the push-forward operator, all reduce to the same actual chain of computations .
Edit intent: coherence
Original:  We further give a short summary of Reverse AD andagain point out the underlying computational steps .
Revised:  We further give a short mathematical description of some methods of higher-order Forward AD and, at the end of this paper, describe the Reverse Mode and explain its relation to the Forward Mode .
Edit intent: clarity
Original:  We further give a short mathematical description of some methods of higher-order Forward AD and, at the end of this paper,  describe the Reverse Mode and explain its relation to the Forward Mode .
Revised:  We further give a short mathematical description of some methods of higher-order Forward AD and, at the end of this paper, describe the Reverse Mode of Automatic Differentiation .
Edit intent: clarity
Original:   We believe that our methods may apply to a range of random CSPs in the 1RSB universality class.
Revised:  We believe that our method may apply to a range of random CSPs in the 1RSB universality class.
Edit intent: fluency
Original:   We believe that our methods may apply to a range of random CSPs in the 1RSB universality class.
Revised:  We believe that our methods may apply to a range of random CSPs in the 1-RSB universality class.
Edit intent: fluency