wanyu/IteraTeR_v2 huggingface dataset:
Original:  Thus, our result generalizes that of Cesati in at least two ways: There is no bound on the size of the tuples of the relations , and the relations do not need to be symmetric.
Revised:  Thus, our result generalizes that of Cesati in at least two ways: The size of the tuples of the relations , and the relations do not need to be symmetric.
Edit intent: clarity
Original:  We study the problem on the Boolean domain, that is 0, 1 . The size of a solution is the number of variables that are mapped to 1. Named by Kolaitis and Vardi (2000), uniform CSP means that the input contains the domain and the list of tuples of each relation in the instance.
Revised:  We study the problem on the Boolean domain, that is 0, . The size of a solution is the number of variables that are mapped to 1. Named by Kolaitis and Vardi (2000), uniform CSP means that the input contains the domain and the list of tuples of each relation in the instance.
Edit intent: coherence
Original:  We study the problem on the Boolean domain, that is 0, 1 . The size of a solution is the number of variables that are mapped to 1. Named by Kolaitis and Vardi (2000), uniform CSP means that the input contains the domain and the list of tuples of each relation in the instance.
Revised:  We study the problem on the Boolean domain, that is 0, 1 we define the size of an assignment as the number of variables that are mapped to 1. Named by Kolaitis and Vardi (2000), uniform CSP means that the input contains the domain and the list of tuples of each relation in the instance.
Edit intent: clarity
Original:  We study the problem on the Boolean domain, that is 0, 1 . The size of a solution is the number of variables that are mapped to 1. Named by Kolaitis and Vardi (2000), uniform CSP means that the input contains the domain and the list of tuples of each relation in the instance.
Revised:  We study the problem on the Boolean domain, that is 0, 1 . The size of a solution is the number of variables that are mapped to a value other than 0. Named by Kolaitis and Vardi (2000), uniform CSP means that the input contains the domain and the list of tuples of each relation in the instance.
Edit intent: clarity
Original:  Uniform CSP restricted to some finite family of Boolean relations (thus with a bound on the arity of relations) can easily be placed in W[1]. Marx (2005) proved that any such problem  is either W[1]-complete or fixed parameter tractable.
Revised:  Uniform CSP restricted to some finite family of relations (thus with a bound on the arity of relations) can easily be placed in W[1]. Marx (2005) proved that any such problem is either W[1]-complete or fixed parameter tractable.
Edit intent: clarity
Original:  Uniform CSP restricted to some finite family of Boolean relations (thus with a bound on the arity of relations) can easily be placed in W[1]. Marx (2005) proved that any such problem  is either W[1]-complete or fixed parameter tractable.
Revised:  Uniform CSP restricted to some finite family of Boolean relations (thus with a bound on the arity of relations) can easily be placed in W[1]. Marx (2005) proved that any such problem over the Boolean domain is either W[1]-complete or fixed parameter tractable.
Edit intent: clarity
Original:  First defined by Chen et al. (2005), such programs characterize W[1] . Our work builds upon the work of Cesati (2002), which, answering a longstanding open question, shows that parameterized Exact Weighted CNF is in W 1%DIFDELCMD < ]%%% . This problem is equivalent to uniform CSP restricted to a specific (infinite) family of Boolean relations, where a tuple is in a relation, if and only if the tuple has exactly one 1.
Revised:  First defined by Chen et al. (2005), such programs characterize W[1] 1%DIFDELCMD < ]%%% . This problem is equivalent to uniform CSP restricted to a specific (infinite) family of Boolean relations, where a tuple is in a relation, if and only if the tuple has exactly one 1.
Edit intent: coherence
Original:  First defined by Chen et al. (2005), such programs characterize W[1] . Our work builds upon the work of Cesati (2002), which, answering a longstanding open question, shows that parameterized Exact Weighted CNF is in W 1%DIFDELCMD < ]%%% . This problem is equivalent to uniform CSP restricted to a specific (infinite) family of Boolean relations, where a tuple is in a relation, if and only if the tuple has exactly one 1.
Revised:  First defined by Chen et al. (2005), such programs characterize W[1] . Our work builds upon the work of Cesati (2002), which, answering a longstanding open question, shows that parameterized Exact Weighted CNF is in W %DIFDELCMD < ]%%% . This problem is equivalent to uniform CSP restricted to a specific (infinite) family of Boolean relations, where a tuple is in a relation, if and only if the tuple has exactly one 1.
Edit intent: coherence
Original:   Uniform CSP restricted to some finite family of relations (thus with a bound on the arity of relations) can easily be placed in W 1%DIFDELCMD < ]%%% . Marx (2005) proved that any such problem over the Boolean domain is either W[1]-complete or fixed parameter tractable.
Revised:  Uniform CSP restricted to some finite family of relations (thus with a bound on the arity of relations) 1%DIFDELCMD < ]%%% . Marx (2005) proved that any such problem over the Boolean domain is either W[1]-complete or fixed parameter tractable.
Edit intent: clarity
Original:   Uniform CSP restricted to some finite family of relations (thus with a bound on the arity of relations) can easily be placed in W 1%DIFDELCMD < ]%%% . Marx (2005) proved that any such problem over the Boolean domain is either W[1]-complete or fixed parameter tractable.
Revised:  Uniform CSP restricted to some finite family of relations (thus with a bound on the arity of relations) can easily be placed in W %DIFDELCMD < ]%%% . Marx (2005) proved that any such problem over the Boolean domain is either W[1]-complete or fixed parameter tractable.
Edit intent: coherence
Original:   Uniform CSP restricted to some finite family of relations (thus with a bound on the arity of relations) can easily be placed in W 1%DIFDELCMD < ]%%% . Marx (2005) proved that any such problem over the Boolean domain is either W[1]-complete or fixed parameter tractable.
Revised:  Uniform CSP restricted to some finite family of relations (thus with a bound on the arity of relations) can easily be placed in W 1%DIFDELCMD < ]%%% and over any finite domain is either W[1]-complete or fixed parameter tractable.
Edit intent: clarity
Original:  We prove that if the weights are bounded by n^k, then the problem is in W[1] . For that, we first prove that parameterized Subset Sum with weights bounded by n^k is in W 1%DIFDELCMD < ]%%% . Abboud et al. (2014) have already proved the later, but our proof is much shorter and arguably more intuitive .
Revised:  We prove that if the weights are bounded by n^k, then the problem is in W[1] 1%DIFDELCMD < ]%%% . Abboud et al. (2014) have already proved the later, but our proof is much shorter and arguably more intuitive .
Edit intent: coherence
Original:  We prove that if the weights are bounded by n^k, then the problem is in W[1] . For that, we first prove that parameterized Subset Sum with weights bounded by n^k is in W 1%DIFDELCMD < ]%%% . Abboud et al. (2014) have already proved the later, but our proof is much shorter and arguably more intuitive .
Revised:  We prove that if the weights are bounded by n^k, then the problem is in W[1] . For that, we first prove that parameterized Subset Sum with weights bounded by n^k is in W %DIFDELCMD < ]%%% . Abboud et al. (2014) have already proved the later, but our proof is much shorter and arguably more intuitive .
Edit intent: clarity
Original:  We prove that if the weights are bounded by n^k, then the problem is in W[1] . For that, we first prove that parameterized Subset Sum with weights bounded by n^k is in W 1%DIFDELCMD < ]%%% . Abboud et al. (2014) have already proved the later, but our proof is much shorter and arguably more intuitive .
Revised:  We prove that if the weights are bounded by n^k, then the problem is in W[1] . For that, we first prove that parameterized Subset Sum with weights bounded by n^k is in W 1%DIFDELCMD < ]%%% .
Edit intent: coherence
Original: We give a structured decomposition for  reversible Boolean functions  . Specifically, an arbitrary n-bit reversible Boolean function is decomposed to 7 blocks of (n-1)-bit Boolean function , where 7 is a constant independent of n;
Revised: We give a structured decomposition for reversible Boolean functions . Specifically, an arbitrary n-bit RBF can be decomposed to 7 blocks of (n-1)-bit Boolean function , where 7 is a constant independent of n;
Edit intent: clarity
Original:  Our  goal is to make standard, ' out-of-the-box' Markov chain Monte Carlo (MCMC) sampling more feasible for complex simulation models  .
Revised:  Our main goal is to make standard, ' out-of-the-box' Markov chain Monte Carlo (MCMC) sampling more feasible for complex simulation models .
Edit intent: coherence
Original:  Our  goal is to make standard, ' out-of-the-box' Markov chain Monte Carlo (MCMC) sampling more feasible for complex simulation models  .
Revised:  Our goal is to make standard, ` out-of-the-box' Markov chain Monte Carlo (MCMC) sampling more feasible for complex simulation models .
Edit intent: fluency
Original:  We then show how to incorporate so-called posterior model approximation error into this hierarchical framework, using a modified form of the Bayesian approximation error (BAE) approach.
Revised:  We then show how to incorporate so-called posterior-informed model approximation error into this hierarchical framework, using a modified form of the Bayesian approximation error (BAE) approach.
Edit intent: clarity
Original:  This enables the use of a ' coarse', approximate model in place of a finer, more expensive model, while also accounting for the additional uncertainty and potential bias that this can introduce.
Revised:  This enables the use of a ` coarse', approximate model in place of a finer, more expensive model, while also accounting for the additional uncertainty and potential bias that this can introduce.
Edit intent: fluency
Original:  This enables the use of a ' coarse', approximate model in place of a finer, more expensive model, while also accounting for the additional uncertainty and potential bias that this can introduce.
Revised:  This enables the use of a ' coarse', approximate model in place of a finer, more expensive model, while accounting for the additional uncertainty and potential bias that this can introduce.
Edit intent: coherence
Original:  Our method requires only simple probability modelling  and only modifies the target posterior - the same standard MCMC sampling algorithm can be used to sample the new target posterior.
Revised:  Our method requires only simple probability modelling and only modifies the target posterior -- any standard MCMC sampling algorithm can be used to sample the new target posterior.
Edit intent: clarity
Original:  We also demonstrate the dangers of naively using coarse, approximate models in place of finer models, without accounting for model discrepancies .
Revised:  We also demonstrate the dangers of naively using coarse, approximate models in place of finer models, without accounting for the induced approximation errors .
Edit intent: clarity
Original:  The naive approach tends to give overly confident and biased posteriors , while incorporating BAE into our hierarchical framework corrects for this while maintaining computational efficiency and ease-of-use.
Revised:  The naive approach tends to give overly confident and biased posteriors while incorporating BAE into our hierarchical framework corrects for this while maintaining computational efficiency and ease-of-use.
Edit intent: fluency
Original: Age-of-information (AoI) is a newly proposed destination-centric performance metric of information freshness.
Revised: Age-of-information (AoI) is a newly proposed performance metric of information freshness.
Edit intent: clarity
Original:  By considering several queueing systems, we show that in certain settings, deterministic service can in fact result in the worst case AoI, while a heavy-tail distributed service can yield the minimum AoI.
Revised:  By considering several queueing systems, we show that in certain settings, deterministic service can in fact result in the worst case AoI, while a heavy-tailed distributed service can yield the minimum AoI.
Edit intent: fluency
Original:  We propose in this paper closed-form approximations for the bid and ask quotes a market maker should set for optimally managing the risk of his/her multi-asset market making book.
Revised:  We propose in this paper closed-form approximations for the value functions of many multi-asset market making book.
Edit intent: clarity
Original:  Furthermore, we propose a perturbative approach to improve our closed-form approximations through Monte-Carlo simulations.
Edit intent: coherence
Original:  Our algorithm is an enabler of the real-time softwarized control of large-scale networks, and not only optical , we believe .
Revised:  Our algorithm is an enabler of real-time softwarized control of large-scale networks, and not only optical , we believe .
Edit intent: fluency
Original:  Our algorithm is an enabler of the real-time softwarized control of large-scale networks, and not only optical , we believe .
Revised:  Our algorithm is an enabler of the real-time softwarized control of large-scale networks, and is not limited to optical networks .
Edit intent: clarity
Original:  We motivate and discuss the algorithm design, and provide our libre, high-quality , and generic implementation using the Boost Graph Library.
Revised:  We motivate and discuss the algorithm design, and provide our free, reliable , and generic implementation using the Boost Graph Library.
Edit intent: clarity
Original:  We carried out 85000 simulation runs for realistic and random networks (Gabriel graphs) of 75 vertices with about a billion shortest-path searches, and found that the proposed algorithm outperforms considerably other three competing optimal algorithms , which are frequently used in research .
Revised:  We carried out 85000 simulation runs for realistic and random networks (Gabriel graphs) of 75 vertices with about a billion shortest-path searches, and found that the proposed algorithm outperforms considerably three other competing optimal algorithms , which are frequently used in research .
Edit intent: fluency
Original:  We carried out 85000 simulation runs for realistic and random networks (Gabriel graphs) of 75 vertices with about a billion shortest-path searches, and found that the proposed algorithm outperforms considerably other three competing optimal algorithms , which are frequently used in research .
Revised:  We carried out 85000 simulation runs for realistic and random networks (Gabriel graphs) of 75 vertices with about a billion shortest-path searches, and found that the proposed algorithm outperforms considerably other three competing optimal algorithms that are frequently used in research .
Edit intent: fluency
Original:  We carried out 85000 simulation runs for realistic and random networks (Gabriel graphs) of 75 vertices with about a billion shortest-path searches, and found that the proposed algorithm outperforms considerably other three competing optimal algorithms , which are frequently used in research .
Revised:  We carried out 85000 simulation runs for realistic and random networks (Gabriel graphs) of 75 vertices with about a billion shortest-path searches, and found that the proposed algorithm outperforms considerably other three competing optimal algorithms , which are frequently used .
Edit intent: clarity
Original:  Assuming the existence of an oracle \Gamma such that \gamma (s) = \Theta\left(  \Gamma(s)\right), we provide an algorithm that reliably performs QAO in time \mathcal{O{\gamma_\min^{-1} \log(\gamma_\min^{-1})} with O{\log(\gamma_\min^{-1})} } \left(}\right) \left()}\right) oracle queries, where \gamma_\min = \min_s \gamma(s).
Revised:  Assuming the existence of an oracle \Gamma such that \gamma _\min = \Theta\left( \Gamma(s)\right), we provide an algorithm that reliably performs QAO in time \mathcal{O{\gamma_\min^{-1} \log(\gamma_\min^{-1})} with O{\log(\gamma_\min^{-1})} } \left(}\right) \left()}\right) oracle queries, where \gamma_\min = \min_s \gamma(s).
Edit intent: clarity
Original:  Assuming the existence of an oracle \Gamma such that \gamma (s) = \Theta\left(  \Gamma(s)\right), we provide an algorithm that reliably performs QAO in time \mathcal{O{\gamma_\min^{-1} \log(\gamma_\min^{-1})} with O{\log(\gamma_\min^{-1})} } \left(}\right) \left()}\right) oracle queries, where \gamma_\min = \min_s \gamma(s).
Revised:  Assuming the existence of an oracle \Gamma such that \gamma (s) = \Theta\left( \min_s \Gamma(s)\right), we provide an algorithm that reliably performs QAO in time \mathcal{O{\gamma_\min^{-1} \log(\gamma_\min^{-1})} with O{\log(\gamma_\min^{-1})} } \left(}\right) \left()}\right) oracle queries, where \gamma_\min = \min_s \gamma(s).
Edit intent: fluency
Original:  Assuming the existence of an oracle \Gamma such that \gamma (s) = \Theta\left(  \Gamma(s)\right), we provide an algorithm that reliably performs QAO in time \mathcal{O{\gamma_\min^{-1} \log(\gamma_\min^{-1})} with O{\log(\gamma_\min^{-1})} } \left(}\right) \left()}\right) oracle queries, where \gamma_\min = \min_s \gamma(s).
Revised:  Assuming the existence of an oracle \Gamma such that \gamma (s) = \Theta\left( \Gamma(s)\right), we provide an algorithm that reliably performs QAO in time \mathcal{O{\gamma_\min^{-1} \log(\gamma_\min^{-1})} with O{\log(\gamma_\min^{-1})} } O\left(}\right) \left()}\right) oracle queries, where \gamma_\min = \min_s \gamma(s).
Edit intent: coherence
Original:  Assuming the existence of an oracle \Gamma such that \gamma (s) = \Theta\left(  \Gamma(s)\right), we provide an algorithm that reliably performs QAO in time \mathcal{O{\gamma_\min^{-1} \log(\gamma_\min^{-1})} with O{\log(\gamma_\min^{-1})} } \left(}\right) \left()}\right) oracle queries, where \gamma_\min = \min_s \gamma(s).
Revised:  Assuming the existence of an oracle \Gamma such that \gamma (s) = \Theta\left( \Gamma(s)\right), we provide an algorithm that reliably performs QAO in time \mathcal{O{\gamma_\min^{-1} \log(\gamma_\min^{-1})} with O{\log(\gamma_\min^{-1})} } \left(\gamma_\min^{-1}\right) \left()}\right) oracle queries, where \gamma_\min = \min_s \gamma(s).
Edit intent: fluency
Original:  Assuming the existence of an oracle \Gamma such that \gamma (s) = \Theta\left(  \Gamma(s)\right), we provide an algorithm that reliably performs QAO in time \mathcal{O{\gamma_\min^{-1} \log(\gamma_\min^{-1})} with O{\log(\gamma_\min^{-1})} } \left(}\right) \left()}\right) oracle queries, where \gamma_\min = \min_s \gamma(s).
Revised:  Assuming the existence of an oracle \Gamma such that \gamma (s) = \Theta\left( \Gamma(s)\right), we provide an algorithm that reliably performs QAO in time \mathcal{O{\gamma_\min^{-1} \log(\gamma_\min^{-1})} with O{\log(\gamma_\min^{-1})} } \left(}\right) with O\left()}\right) oracle queries, where \gamma_\min = \min_s \gamma(s).
Edit intent: fluency
Original:  Assuming the existence of an oracle \Gamma such that \gamma (s) = \Theta\left(  \Gamma(s)\right), we provide an algorithm that reliably performs QAO in time \mathcal{O{\gamma_\min^{-1} \log(\gamma_\min^{-1})} with O{\log(\gamma_\min^{-1})} } \left(}\right) \left()}\right) oracle queries, where \gamma_\min = \min_s \gamma(s).
Revised:  Assuming the existence of an oracle \Gamma such that \gamma (s) = \Theta\left( \Gamma(s)\right), we provide an algorithm that reliably performs QAO in time \mathcal{O{\gamma_\min^{-1} \log(\gamma_\min^{-1})} with O{\log(\gamma_\min^{-1})} } \left(}\right) \left(\log(\gamma_\min^{-1)}\right) oracle queries, where \gamma_\min = \min_s \gamma(s).
Edit intent: fluency
Original:  Rather, our algorithm naturally produces an annealing path such that  dH/ds  \approx \gamma(s) and chooses its own runtime T to be as close as possible to optimal while promising convergence to the ground state.
Revised:  Rather, our algorithm naturally produces an annealing path such that dH/ds \approx \gamma(s) and chooses its own runtime to be as close as possible to optimal while promising convergence to the ground state.
Edit intent: clarity
Original:  We then demonstrate the feasibility of this approach in practice by explicitly constructing a gap oracle \Gamma for the problem of finding a vertex m = argmin_u W(u) of the cost function W:V\longrightarrow [0,1], restricting ourselves to computational basis measurements and driving Hamiltonian H(0)=I -
Revised:  We then demonstrate the feasibility of this approach in practice by explicitly constructing a gap oracle \Gamma for the problem of finding the minimum point m = argmin_u W(u) of the cost function W:V\longrightarrow [0,1], restricting ourselves to computational basis measurements and driving Hamiltonian H(0)=I -
Edit intent: clarity
Original:  V ^{-1}u,v \in \mathcal{V} |u \vert{u} \rangle %DIFDELCMD < \langle %%% v |, with V = |\mathcal{V \langle{v}\vert . Requiring only that W have a constant lower bound on its spectral gap and upper bound \kappa on its spectral ratio, our QAO algorithm returns m using \Gamma with probability (1-\epsilon)(1-e^{-1/\epsilon}) in time \widetilde{\mathcal{O}}(\epsilon ^{-1[\sqrt{V} + (\kappa-1)^{2/3}V^{2/3}]} [\sqrt{|\mathcal{V}|} + (\kappa-1)^{2/3}|\mathcal{V}|^{2/3}]} ).
Revised:  |\mathcal{V ^{-1}u,v \in \mathcal{V} |u \vert{u} \rangle %DIFDELCMD < \langle %%% v |, with V = |\mathcal{V \langle{v}\vert . Requiring only that W have a constant lower bound on its spectral gap and upper bound \kappa on its spectral ratio, our QAO algorithm returns m using \Gamma with probability (1-\epsilon)(1-e^{-1/\epsilon}) in time \widetilde{\mathcal{O}}(\epsilon ^{-1[\sqrt{V} + (\kappa-1)^{2/3}V^{2/3}]} [\sqrt{|\mathcal{V}|} + (\kappa-1)^{2/3}|\mathcal{V}|^{2/3}]} ).
Edit intent: fluency
Original:  V ^{-1}u,v \in \mathcal{V} |u \vert{u} \rangle %DIFDELCMD < \langle %%% v |, with V = |\mathcal{V \langle{v}\vert . Requiring only that W have a constant lower bound on its spectral gap and upper bound \kappa on its spectral ratio, our QAO algorithm returns m using \Gamma with probability (1-\epsilon)(1-e^{-1/\epsilon}) in time \widetilde{\mathcal{O}}(\epsilon ^{-1[\sqrt{V} + (\kappa-1)^{2/3}V^{2/3}]} [\sqrt{|\mathcal{V}|} + (\kappa-1)^{2/3}|\mathcal{V}|^{2/3}]} ).
Revised:  V ^{-1}u,v \in \mathcal{V} \vert{u} \rangle %DIFDELCMD < \langle %%% v |, with V = |\mathcal{V \langle{v}\vert . Requiring only that W have a constant lower bound on its spectral gap and upper bound \kappa on its spectral ratio, our QAO algorithm returns m using \Gamma with probability (1-\epsilon)(1-e^{-1/\epsilon}) in time \widetilde{\mathcal{O}}(\epsilon ^{-1[\sqrt{V} + (\kappa-1)^{2/3}V^{2/3}]} [\sqrt{|\mathcal{V}|} + (\kappa-1)^{2/3}|\mathcal{V}|^{2/3}]} ).
Edit intent: clarity
Original:  V ^{-1}u,v \in \mathcal{V} |u \vert{u} \rangle %DIFDELCMD < \langle %%% v |, with V = |\mathcal{V \langle{v}\vert . Requiring only that W have a constant lower bound on its spectral gap and upper bound \kappa on its spectral ratio, our QAO algorithm returns m using \Gamma with probability (1-\epsilon)(1-e^{-1/\epsilon}) in time \widetilde{\mathcal{O}}(\epsilon ^{-1[\sqrt{V} + (\kappa-1)^{2/3}V^{2/3}]} [\sqrt{|\mathcal{V}|} + (\kappa-1)^{2/3}|\mathcal{V}|^{2/3}]} ).
Revised:  V ^{-1}u,v \in \mathcal{V} |u \vert{u} \rangle %DIFDELCMD < \langle %%% \langle{v}\vert . Requiring only that W have a constant lower bound on its spectral gap and upper bound \kappa on its spectral ratio, our QAO algorithm returns m using \Gamma with probability (1-\epsilon)(1-e^{-1/\epsilon}) in time \widetilde{\mathcal{O}}(\epsilon ^{-1[\sqrt{V} + (\kappa-1)^{2/3}V^{2/3}]} [\sqrt{|\mathcal{V}|} + (\kappa-1)^{2/3}|\mathcal{V}|^{2/3}]} ).
Edit intent: clarity