wanyu/IteraTeR_v2 huggingface dataset:
Original:  We give semantics to these Stateful NetKAT programs in terms of NESs, develop general mechanisms for implementing NESs using next-generation switches, and prove our implementation strategies correct.
Revised:  We give semantics to these Stateful NetKAT programs in terms of NESs, develop general mechanisms for implementing NESs using SDN switches, and prove our implementation strategies correct.
Edit intent: clarity
Original:  We give semantics to these Stateful NetKAT programs in terms of NESs, develop general mechanisms for implementing NESs using next-generation switches, and prove our implementation strategies correct.
Revised:  We give semantics to these Stateful NetKAT programs in terms of NESs, develop general mechanisms for implementing NESs using next-generation switches, and prove them correct.
Edit intent: clarity
Original:  Existing SDN platforms offer weak guarantees that often break application invariants, leading to problems such as dropped packets, degraded performance, security violations, etc.
Revised:  Existing SDN platforms offer weak guarantees that can break application invariants, leading to problems such as dropped packets, degraded performance, security violations, etc.
Edit intent: clarity
Original:  This paper introduces event-driven consistent updates that are guaranteed to preserve well-defined behaviors when transitioning between configurations in response to events.
Revised:  This paper introduces EVENT-DRIVEN CONSISTENT UPDATES that are guaranteed to preserve well-defined behaviors when transitioning between configurations in response to events.
Edit intent: fluency
Original:  We propose network event structures (NESs) to model constraints on updates, such as which events can be enabled simultaneously and causal dependencies between events.
Revised:  We propose NETWORK EVENT STRUCTURES (NESs) to model constraints on updates, such as which events can be enabled simultaneously and causal dependencies between events.
Edit intent: fluency
Original:  We define an extension of the NetKAT language with mutable state, and give semantics to stateful programs using NESs . We discuss strategies for implementing NESs using SDN switches, and prove them correct .
Revised:  We define an extension of the NetKAT language with mutable state, give semantics to stateful programs using NESs . We discuss strategies for implementing NESs using SDN switches, and prove them correct .
Edit intent: fluency
Original:  We define an extension of the NetKAT language with mutable state, and give semantics to stateful programs using NESs . We discuss strategies for implementing NESs using SDN switches, and prove them correct .
Revised:  We define an extension of the NetKAT language with mutable state, and give semantics to stateful programs using NESs , and discuss provably-correct strategies for implementing NESs using SDN switches, and prove them correct .
Edit intent: clarity
Original:  We define an extension of the NetKAT language with mutable state, and give semantics to stateful programs using NESs . We discuss strategies for implementing NESs using SDN switches, and prove them correct .
Revised:  We define an extension of the NetKAT language with mutable state, and give semantics to stateful programs using NESs . We discuss strategies for implementing NESs in SDNs .
Edit intent: coherence
Original: In this paper I address the question - how large is a phylogenetic sample ? I propose a definition of a phylogenetic effective sample size for Brownian motion and Ornstein-Uhlenbeck processes - the regression effective sample size.
Revised: In this paper I address the question - how large is a phylogenetic sample I propose a definition of a phylogenetic effective sample size for Brownian motion and Ornstein-Uhlenbeck processes - the regression effective sample size.
Edit intent: fluency
Original: We develop an agent-based model to reproduce the process of link formation and to understand the effect of knowledge exchange in collaborative inter-firm networks of Research and Development (  R&D ) alliances .
Revised: We propose a model that reflects two important processes in R R&D ) alliances .
Edit intent: clarity
Original:  We find that real R&D alliances have a duration of around two years , and that the subsequent knowledge exchange occurs at an extremely low rate- a firm's position  is rather a determinant than a consequence of its R&D alliances.
Revised:  We find that R&D alliances have a duration of around two years , and that the subsequent knowledge exchange occurs at an extremely low rate- a firm's position is rather a determinant than a consequence of its R&D alliances.
Edit intent: clarity
Original:  We find that real R&D alliances have a duration of around two years , and that the subsequent knowledge exchange occurs at an extremely low rate- a firm's position  is rather a determinant than a consequence of its R&D alliances.
Revised:  We find that real R&D alliances have a duration of around two years and that the subsequent knowledge exchange occurs at an extremely low rate- a firm's position is rather a determinant than a consequence of its R&D alliances.
Edit intent: fluency
Original:  We find that real R&D alliances have a duration of around two years , and that the subsequent knowledge exchange occurs at an extremely low rate- a firm's position  is rather a determinant than a consequence of its R&D alliances.
Revised:  We find that real R&D alliances have a duration of around two years , and that the subsequent knowledge exchange occurs at a very low rate. Hence, a firm's position is rather a determinant than a consequence of its R&D alliances.
Edit intent: coherence
Original:  We find that real R&D alliances have a duration of around two years , and that the subsequent knowledge exchange occurs at an extremely low rate- a firm's position  is rather a determinant than a consequence of its R&D alliances.
Revised:  We find that real R&D alliances have a duration of around two years , and that the subsequent knowledge exchange occurs at an extremely low rate- a firm's position in the knowledge space is rather a determinant than a consequence of its R&D alliances.
Edit intent: clarity
Original:  Finally, we propose an indicator of collaboration performance for the whole network and, remarkably, we find that the empirical R D network extracted from our data does not maximize such an indicator.
Revised:  D network extracted from our data does not maximize such an indicator.
Edit intent: coherence
Original:  However, we find that there exist configurations that can be both realistic and optimized with respect to the collaboration performance . Effective policies, as suggested by our model, would incentivize shorter R&D alliances and higher knowledge exchange rates.
Revised:  However, we find that there exist configurations that can be both realistic and optimized with respect to the collaboration efficiency \mathcal{\hat{C . Effective policies, as suggested by our model, would incentivize shorter R&D alliances and higher knowledge exchange rates.
Edit intent: clarity
Original:  In our model, we represent users' applications running on different user equipments (UE)s by logarithmic and sigmoidal-like utility functions.
Revised:  In our model, we represent users' applications running on different user equipments (UE)s by logarithmic and sigmoid utility functions.
Edit intent: clarity
Original:  We prove that the novel resource allocation optimization problem with frequency reuse is convex and therefore the optimal solution is tractable.
Revised:  We show that the novel resource allocation optimization problem with frequency reuse is convex and therefore the optimal solution is tractable.
Edit intent: coherence
Original:  We present a distributed algorithm to allocate the resources optimally from Mobility Management Entity (MME) to evolved NodeBs' (eNodeB )s sectors.
Revised:  We present a distributed algorithm to allocate the resources optimally from Mobility Management Entity (MME) to base stations (BS )s sectors.
Edit intent: clarity
Original: Look at the quality-driven success of manufactured goods .
Revised: Wherever we look, we see numerous success stories of quality-designed products .
Edit intent: clarity
Original:  A positive answer to this question leads us to Quantitative Structuring -- a technology of manufacturing  financial products.
Revised:  This paper is a fast introduction to Quantitative Structuring -- a technology of manufacturing financial products.
Edit intent: coherence
Original:  This paper is a fast introduction into Quantitative Structuring.
Edit intent: coherence
Original:  Further details are given in the form of references to specific results including applications beyond product design: from model risk to economics.
Revised:  A short summary with references provide further depth and also cover applications beyond product design: from model risk to economics.
Edit intent: clarity
Original: Wherever we look, we see numerous success stories of quality-designed products .
Revised: Quality-designed products are easy to recognize .
Edit intent: clarity
Original:  More detailed discussions are presented as a set of appendices .
Revised:  More detailed discussions are arranged as a set of appendices .
Edit intent: clarity
Original: Quality-designed  products are easy to recognize.
Revised: Quality-designed consumer products are easy to recognize.
Edit intent: clarity
Original: Determining the trace of a matrix that is implicitly available through a function is a computationally challenging task that arises in a number of applications.
Revised: A number of applications require the computation of the trace of a matrix that is implicitly available through a function is a computationally challenging task that arises in a number of applications.
Edit intent: clarity
Original:  We present a different approach by exploiting the pattern correlation  between the diagonal of the inverse of the matrix and the diagonal of some approximate inverse that can be computed inexpensively.
Revised:  We present a different approach that exploits the pattern correlation between the diagonal of the inverse of the matrix and the diagonal of some approximate inverse that can be computed inexpensively.
Edit intent: coherence
Original:   An extensive set of experiments with various technique combinations demonstrates the effectiveness of our method in some real applications .
Revised:  An extensive set of experiments with various technique combinations on several matrices from some real applications demonstrate the potential of our method in some real applications .
Edit intent: clarity
Original:   An extensive set of experiments with various technique combinations demonstrates the effectiveness of our method in some real applications .
Revised:  An extensive set of experiments with various technique combinations demonstrates the effectiveness of our method .
Edit intent: clarity
Original:  Convergence of the algorithms is proved and the rate of convergence is analysed under the \L ojasiewicz property of the objective function.
Revised:  Convergence of the algorithms is proved and the rate of convergence is analysed under the ojasiewicz property of the objective function.
Edit intent: fluency
Original:  Convergence of the algorithms is proved and the rate of convergence is analysed under the \L ojasiewicz property of the objective function.
Revised:  Convergence of the algorithms is proved and the rate of convergence is analysed under the \L Lojasiewicz property of the objective function.
Edit intent: fluency
Original:  We apply our algorithms to a class of smooth DC programs arising in the study of biochemical reaction networks, where the objective function is real analytic and thus satisfies the \L ojasiewicz property.
Revised:  We apply our algorithms to a class of smooth DC programs arising in the study of biochemical reaction networks, where the objective function is real analytic and thus satisfies the ojasiewicz property.
Edit intent: fluency
Original:  We apply our algorithms to a class of smooth DC programs arising in the study of biochemical reaction networks, where the objective function is real analytic and thus satisfies the \L ojasiewicz property.
Revised:  We apply our algorithms to a class of smooth DC programs arising in the study of biochemical reaction networks, where the objective function is real analytic and thus satisfies the \L Lojasiewicz property.
Edit intent: fluency
Original:  The algorithms are globally convergent to a non-equilibrium steady state of a biochemical network , with only chemically consistent restrictions on the network topology.
Revised:  The algorithms are globally convergent to a non-equilibrium steady state of various biochemical networks , with only chemically consistent restrictions on the network topology.
Edit intent: clarity
Original:  The metric is shown to be correlated with the geometric dilution of precision (GDOP), yet has the benefit of being characterizable in terms of the network parameters for BS layouts modeled according to a Poisson point process  .
Revised:  The metric is shown to be closely related to the geometric-dilution-of-precision (GDOP), yet has the benefit of being characterizable in terms of the network parameters for BS layouts modeled according to a Poisson point process .
Edit intent: clarity
Original: We propose the first unified framework that yields an improved sparsification algorithm for computing in nearly linear time a spectral sparsifier D-M_{N} for any matrix-polynomial of the form%DIFDELCMD < \[ %DIFDELCMD < D-M_{N}\epsilonD-Di=0^{N}i(D^{-1} M)^i \]
Revised: We propose a simple, faster and unified algorithm that computes in nearly linear time a spectral sparsifier D-M_{N} for any matrix-polynomial of the form%DIFDELCMD < \[ %DIFDELCMD < D-M_{N}\epsilonD-Di=0^{N}i(D^{-1} M)^i \]
Edit intent: clarity
Original: We propose the first unified framework that yields an improved sparsification algorithm for computing in nearly linear time a spectral sparsifier D-M_{N} for any matrix-polynomial of the form%DIFDELCMD < \[ %DIFDELCMD < D-M_{N}\epsilonD-Di=0^{N}i(D^{-1} M)^i \]
Revised: We propose the first unified framework that yields an improved sparsification algorithm for computing in nearly linear time a spectral sparsifier D-M_{N} %DIFDELCMD < \[ %DIFDELCMD < D-M_{N}\epsilonD-Di=0^{N}i(D^{-1} M)^i \]
Edit intent: coherence
Original:  %DIFDELCMD < %%%  where B=D-M\inR^{n\times n} is either Laplacian or SDDM matrix with m_B non-zero entries, and the vector%DIFDELCMD < \gammais %%%  induced by a mixture of discrete Binomial distributions (MDBD) . Our sparsification algorithm runs in time O( \epsilon ^{-2}m_B\log^{3}n\cdot\log^{2}N + \epsilon^{-4\cdot nN\cdot}  \log^{4}n\cdot\log^{5}N) \footnote{\widetilde{O} and exhibits a significant improvement over the  result of Cheng et al.
Revised:  %DIFDELCMD < %%% where B=D-M\inR^{n\times n} is either Laplacian or SDDM matrix with m_B non-zero entries, %DIFDELCMD < \gammais %%% induced by a mixture of discrete Binomial distributions (MDBD) . Our sparsification algorithm runs in time O( \epsilon ^{-2}m_B\log^{3}n\cdot\log^{2}N + \epsilon^{-4\cdot nN\cdot} \log^{4}n\cdot\log^{5}N) \footnote{\widetilde{O} and exhibits a significant improvement over the result of Cheng et al.
Edit intent: coherence
Original:  %DIFDELCMD < %%%  where B=D-M\inR^{n\times n} is either Laplacian or SDDM matrix with m_B non-zero entries, and the vector%DIFDELCMD < \gammais %%%  induced by a mixture of discrete Binomial distributions (MDBD) . Our sparsification algorithm runs in time O( \epsilon ^{-2}m_B\log^{3}n\cdot\log^{2}N + \epsilon^{-4\cdot nN\cdot}  \log^{4}n\cdot\log^{5}N) \footnote{\widetilde{O} and exhibits a significant improvement over the  result of Cheng et al.
Revised:  %DIFDELCMD < %%% where B=D-M\inR^{n\times n} is either Laplacian or SDDM matrix with m_B non-zero entries, and the vector%DIFDELCMD < \gammais %%% induced by a mixture of discrete Binomial distributions (MDBD) . Our sparsification algorithm runs in time O( \varepsilon ^{-2}m_B\log^{3}n\cdot\log^{2}N + \epsilon^{-4\cdot nN\cdot} \log^{4}n\cdot\log^{5}N) \footnote{\widetilde{O} and exhibits a significant improvement over the result of Cheng et al.
Edit intent: fluency
Original:  %DIFDELCMD < %%%  where B=D-M\inR^{n\times n} is either Laplacian or SDDM matrix with m_B non-zero entries, and the vector%DIFDELCMD < \gammais %%%  induced by a mixture of discrete Binomial distributions (MDBD) . Our sparsification algorithm runs in time O( \epsilon ^{-2}m_B\log^{3}n\cdot\log^{2}N + \epsilon^{-4\cdot nN\cdot}  \log^{4}n\cdot\log^{5}N) \footnote{\widetilde{O} and exhibits a significant improvement over the  result of Cheng et al.
Revised:  %DIFDELCMD < %%% where B=D-M\inR^{n\times n} is either Laplacian or SDDM matrix with m_B non-zero entries, and the vector%DIFDELCMD < \gammais %%% induced by a mixture of discrete Binomial distributions (MDBD) . Our sparsification algorithm runs in time O( \epsilon ^{-2}m_B\log^{3}n\cdot\log^{2}N + \epsilon^{-4\cdot nN\cdot} \log^{4}n\cdot\log^{5}N) \footnote{We use the\widetilde{O} and exhibits a significant improvement over the result of Cheng et al.
Edit intent: coherence
Original: [CCLPT15] whose running time is \widetilde{O}( \epsilon^{-2\cdot }  m_B N^2 \cdot \mathrm{poly}(\log n)).
Revised: [CCLPT15] whose run time is \widetilde{O}( \epsilon^{-2\cdot } m_B N^2 \cdot \mathrm{poly}(\log n)).
Edit intent: fluency
Original: [CCLPT15] whose running time is \widetilde{O}( \epsilon^{-2\cdot }  m_B N^2 \cdot \mathrm{poly}(\log n)).
Revised: [CCLPT15] whose running time is \widetilde{O}( \epsilon^{-2\cdot } m_B N^2 \mathrm{poly}(\log n)).
Edit intent: fluency
Original:  Although their algorithm handles general probability distributions, we show that MDBD approximate large class of continuous probability distributions.
Revised:  Although their algorithm handles general probability distributions, we demonstrate that MDBD approximate large class of continuous probability distributions.
Edit intent: clarity
Original:  } time a spectral sparsifier D- _{N \approx}  \approx} _{ \varepsilon } D-D\sum_{i=0}^{N} \gamma _{i}(D^{-1} M)^i of matrix-polynomials, where B=D-M\in\mathbb{R^{n\times n} is either Laplacian or SDDM matrix with m_B non-zero entries, the coefficients \gamma_i are induced by a mixture of discrete Binomial distributions MDBD, and N=2^k for k\in\mathbb{N}.
Revised:  } time a spectral sparsifier D- \approx} \approx} _{ \varepsilon } D-D\sum_{i=0}^{N} \gamma _{i}(D^{-1} M)^i of matrix-polynomials, where B=D-M\in\mathbb{R^{n\times n} is either Laplacian or SDDM matrix with m_B non-zero entries, the coefficients \gamma_i are induced by a mixture of discrete Binomial distributions MDBD, and N=2^k for k\in\mathbb{N}.
Edit intent: fluency
Original:  } time a spectral sparsifier D- _{N \approx}  \approx} _{ \varepsilon } D-D\sum_{i=0}^{N} \gamma _{i}(D^{-1} M)^i of matrix-polynomials, where B=D-M\in\mathbb{R^{n\times n} is either Laplacian or SDDM matrix with m_B non-zero entries, the coefficients \gamma_i are induced by a mixture of discrete Binomial distributions MDBD, and N=2^k for k\in\mathbb{N}.
Revised:  } time a spectral sparsifier D- _{N \approx} _{N \approx} _{ \varepsilon } D-D\sum_{i=0}^{N} \gamma _{i}(D^{-1} M)^i of matrix-polynomials, where B=D-M\in\mathbb{R^{n\times n} is either Laplacian or SDDM matrix with m_B non-zero entries, the coefficients \gamma_i are induced by a mixture of discrete Binomial distributions MDBD, and N=2^k for k\in\mathbb{N}.
Edit intent: fluency
Original:  } time a spectral sparsifier D- _{N \approx}  \approx} _{ \varepsilon } D-D\sum_{i=0}^{N} \gamma _{i}(D^{-1} M)^i of matrix-polynomials, where B=D-M\in\mathbb{R^{n\times n} is either Laplacian or SDDM matrix with m_B non-zero entries, the coefficients \gamma_i are induced by a mixture of discrete Binomial distributions MDBD, and N=2^k for k\in\mathbb{N}.
Revised:  } time a spectral sparsifier D- _{N \approx} \approx} _{ \epsilon } D-D\sum_{i=0}^{N} \gamma _{i}(D^{-1} M)^i of matrix-polynomials, where B=D-M\in\mathbb{R^{n\times n} is either Laplacian or SDDM matrix with m_B non-zero entries, the coefficients \gamma_i are induced by a mixture of discrete Binomial distributions MDBD, and N=2^k for k\in\mathbb{N}.
Edit intent: clarity
Original:  Our sparsification algorithm runs in time }%DIFDELCMD < \widetilde{O}%%% (\varepsilon^{-2m_B\log^{3}n\cdot\log^{2}} \hat{O}(\log n,\log } N + \varepsilon^{-4nN\log^{4}n\cdot\log ^{5}N) }\footnote{We use the%DIFDELCMD < \widetilde{O}%%% (\cdot) notation to hide (\log\log n)^{3 factors.
Revised:  Our sparsification algorithm runs in time }%DIFDELCMD < \widetilde{O}%%% m_B\log^{3}n\cdot\log^{2}} \hat{O}(\log n,\log } N + \varepsilon^{-4nN\log^{4}n\cdot\log ^{5}N) }\footnote{We use the%DIFDELCMD < \widetilde{O}%%% (\cdot) notation to hide (\log\log n)^{3 factors.
Edit intent: coherence
Original:  Our sparsification algorithm runs in time }%DIFDELCMD < \widetilde{O}%%% (\varepsilon^{-2m_B\log^{3}n\cdot\log^{2}} \hat{O}(\log n,\log } N + \varepsilon^{-4nN\log^{4}n\cdot\log ^{5}N) }\footnote{We use the%DIFDELCMD < \widetilde{O}%%% (\cdot) notation to hide (\log\log n)^{3 factors.
Revised:  Our sparsification algorithm runs in time }%DIFDELCMD < \widetilde{O}%%% (\varepsilon^{-2m_B\log^{3}n\cdot\log^{2}} \hat{O}(\log n,\log } N + \varepsilon^{-4nN\log^{4}n\cdot\log ^{5}N) }\footnote{%DIFDELCMD < \widetilde{O}%%% (\cdot) notation to hide (\log\log n)^{3 factors.
Edit intent: coherence
Original:  Our sparsification algorithm runs in time }%DIFDELCMD < \widetilde{O}%%% (\varepsilon^{-2m_B\log^{3}n\cdot\log^{2}} \hat{O}(\log n,\log } N + \varepsilon^{-4nN\log^{4}n\cdot\log ^{5}N) }\footnote{We use the%DIFDELCMD < \widetilde{O}%%% (\cdot) notation to hide (\log\log n)^{3 factors.
Revised:  Our sparsification algorithm runs in time }%DIFDELCMD < \widetilde{O}%%% (\varepsilon^{-2m_B\log^{3}n\cdot\log^{2}} \hat{O}(\log n,\log } N + \varepsilon^{-4nN\log^{4}n\cdot\log ^{5}N) }\footnote{We use the%DIFDELCMD < \widetilde{O}%%% factors.
Edit intent: coherence
Original:  In addition, we show that a simple preprocessing step speeds up the run time of Spielman and Peng's PS14%DIFDELCMD < ] %%% SDDM Solver from%DIFDELCMD < \widetilde{O}%%% (m_B\log ^{3n\cdot} \hat{O}m + \epsilon^{-4}nT)
Revised:  In addition, we show that a simple preprocessing step speeds up the run time of Spielman and Peng's %DIFDELCMD < ] %%% SDDM Solver from%DIFDELCMD < \widetilde{O}%%% (m_B\log ^{3n\cdot} \hat{O}m + \epsilon^{-4}nT)
Edit intent: clarity
Original:  and depth O(\log N\cdot\mathrm{poly}(} \log ^{2\kappa_B) to }%DIFDELCMD < \widetilde{O}%%% (m_{B\log ^{2}n}  + n\log ^{4n\cdot\log^{5}\kappa_B), where \kappa_B is } , matrix B=D-M as above, outputs a spectral sparsifier of matrix-polynomial whose coefficients approximate component-wise the discretized p.d.f. }\hat{w} the condition number of the input SDDM matrix B.
Revised:  and depth O(\log N\cdot\mathrm{poly}(} \log \kappa_B) to }%DIFDELCMD < \widetilde{O}%%% (m_{B\log ^{2}n} + n\log ^{4n\cdot\log^{5}\kappa_B), where \kappa_B is } , matrix B=D-M as above, outputs a spectral sparsifier of matrix-polynomial whose coefficients approximate component-wise the discretized p.d.f. }\hat{w} the condition number of the input SDDM matrix B.
Edit intent: fluency
Original:  and depth O(\log N\cdot\mathrm{poly}(} \log ^{2\kappa_B) to }%DIFDELCMD < \widetilde{O}%%% (m_{B\log ^{2}n}  + n\log ^{4n\cdot\log^{5}\kappa_B), where \kappa_B is } , matrix B=D-M as above, outputs a spectral sparsifier of matrix-polynomial whose coefficients approximate component-wise the discretized p.d.f. }\hat{w} the condition number of the input SDDM matrix B.
Revised:  and depth O(\log N\cdot\mathrm{poly}(} \log ^{2\kappa_B) to }%DIFDELCMD < \widetilde{O}%%% \log ^{2}n} + n\log ^{4n\cdot\log^{5}\kappa_B), where \kappa_B is } , matrix B=D-M as above, outputs a spectral sparsifier of matrix-polynomial whose coefficients approximate component-wise the discretized p.d.f. }\hat{w} the condition number of the input SDDM matrix B.
Edit intent: coherence