wanyu/IteraTeR_v2 huggingface dataset:
Original: We derive a simple criterion that ensures uniqueness, Lipschitz stability and global convergence of Newton's method for finite dimensional inverse problems with a continuously differentiable, componentwise convex and monotonic forward function.
Revised: We derive a simple criterion that ensures uniqueness, Lipschitz stability and global convergence of Newton's method for finite dimensional inverse problems with a continuously differentiable, componentwise convex and monotonic function.
Edit intent: clarity
Original:  Our criterion merely requires to evaluate the directional derivative of the forward function at finitely many evaluation points and  finitely many directions.
Revised:  Our criterion merely requires to evaluate the directional derivative of the forward function at finitely many evaluation points and for finitely many directions.
Edit intent: clarity
Original:   Using a relation to monotonicity and localized potentials techniques for inverse coefficient problems in elliptic PDEs, we will then show that a discretized inverse Robin transmission problem always fulfills our criterion if enough measurements are being used.
Revised:  Using a relation to monotonicity and localized potentials techniques , we show that a discretized inverse Robin transmission problem always fulfills our criterion if enough measurements are being used.
Edit intent: coherence
Original:  Thus our result enables us to determine those boundary measurements from which an unknown coefficient can be uniquely and stably reconstructed with a given desired resolution by a globally convergent Newton iteration  .
Revised:  Thus our result enables us to determine those boundary measurements from which an unknown coefficient can be uniquely and stably reconstructed by a globally convergent Newton iteration .
Edit intent: clarity
Original: GTIRB is an intermediate representation for binary analysis and transformation tools including disassemblers, lifters, analyzers, rewriters, and pretty-printers.
Revised: GTIRB is an intermediate representation for binary analysis and rewriting tools including disassemblers, lifters, analyzers, rewriters, and pretty-printers.
Edit intent: clarity
Original:  GTIRB is designed to enable communication between tools in a format that ensures the basic information necessary for analysis and rewriting is provided while making no further assumptions about domain (e.g., malware vs. cleanware, or PE vs. ELF) or semantic interpretation (functional vs. operational semantics).
Revised:  GTIRB is designed to enable communication between tools in a format that provides the basic information necessary for analysis and rewriting is provided while making no further assumptions about domain (e.g., malware vs. cleanware, or PE vs. ELF) or semantic interpretation (functional vs. operational semantics).
Edit intent: clarity
Original:  GTIRB is designed to enable communication between tools in a format that ensures the basic information necessary for analysis and rewriting is provided while making no further assumptions about domain (e.g., malware vs. cleanware, or PE vs. ELF) or semantic interpretation (functional vs. operational semantics).
Revised:  GTIRB is designed to enable communication between tools in a format that ensures the basic information necessary for analysis and rewriting while making no further assumptions about domain (e.g., malware vs. cleanware, or PE vs. ELF) or semantic interpretation (functional vs. operational semantics).
Edit intent: clarity
Original:  This design supports the goals of (1) encouraging tool modularization and re-use allowing researchers and developers to focus on a single aspect of binary analysis and rewriting without committing to any single tool chain and (2) easing communication and comparison between tools.
Revised:  This design supports the goals of (1) encouraging tool modularization and re-use allowing researchers and developers to focus on a single aspect of binary analysis and rewriting without committing to any single tool chain and (2) facilitating communication and comparison between tools.
Edit intent: clarity
Original:  Sakoda and Sipser [STOC 1972, pp. 275-286] were concerned with nonuniform families of finite automata and they discussed the behaviors of nonuniform complexity classes defined by families of such finite automata having polynomial-size state complexity.
Revised:  Sakoda and Sipser [STOC 1972, pp. 275-286] were concerned with nonuniform families of finite automata and they discussed the behaviors of nonuniform complexity classes defined by such families of finite automata having polynomial-size state complexity.
Edit intent: fluency
Original:  In a similar fashion, we introduce nonuniform state complexity classes using  families of quantum finite automata .
Revised:  In a similar fashion, we introduce nonuniform state complexity classes using nonuniform families of quantum finite automata .
Edit intent: fluency
Original:  We  show inclusion and separation relationships among nonuniform state complexity classes of various one-way finite automata, including deterministic, nondeterministic, probabilistic, and quantum finite automata of polynomial size .
Revised:  We first show inclusion and separation relationships among nonuniform state complexity classes of various one-way finite automata, including deterministic, nondeterministic, probabilistic, and quantum finite automata of polynomial size .
Edit intent: coherence
Original:  We  show inclusion and separation relationships among nonuniform state complexity classes of various one-way finite automata, including deterministic, nondeterministic, probabilistic, and quantum finite automata of polynomial size .
Revised:  We show inclusion and separation relationships among nonuniform state complexity classes of various one-way finite automata, including deterministic, nondeterministic, probabilistic, and quantum finite automata having polynomially many inner states .
Edit intent: clarity
Original:  For two-way quantum finite automata equipped with  garbage tapes, we discover a close relationship between the nonuniform state complexity of such a polynomial-size quantum finite automata family and the parameterized complexity class induced by quantum logarithmic-space computation assisted by polynomial-size advice  .
Revised:  For two-way quantum finite automata equipped with garbage tapes, we present a close relationship between the nonuniform state complexity of such a polynomial-size quantum finite automata family and the parameterized complexity class induced by quantum logarithmic-space computation assisted by polynomial-size advice .
Edit intent: clarity
Original:  Sakoda and Sipser [STOC 1972, pp. 275-286 ] were concerned with nonuniform families of finite automata and they discussed the behaviors of  nonuniform complexity classes defined by such families of finite automata having polynomial-size state complexity.
Revised:  Sakoda and Sipser [STOC 1972, pp. 275--286 ] were concerned with nonuniform families of finite automata and they discussed the behaviors of nonuniform complexity classes defined by such families of finite automata having polynomial-size state complexity.
Edit intent: clarity
Original:  Sakoda and Sipser [STOC 1972, pp. 275-286 ] were concerned with nonuniform families of finite automata and they discussed the behaviors of  nonuniform complexity classes defined by such families of finite automata having polynomial-size state complexity.
Revised:  Sakoda and Sipser [STOC 1972, pp. 275-286 ] were concerned with nonuniform families of finite automata and they discussed the behaviors of the nonuniform complexity classes defined by such families of finite automata having polynomial-size state complexity.
Edit intent: fluency
Original:  For two-way quantum finite automata equipped with flexible garbage tapes, we present a close relationship between the nonuniform state complexity of  such a polynomial-size quantum finite automata family and the parameterized complexity class induced by quantum logarithmic-space computation assisted by polynomial-size advice.
Revised:  For two-way quantum finite automata equipped with flexible garbage tapes, we present a close relationship between the nonuniform state complexity of such a polynomial-size quantum finite automata and the parameterized complexity class induced by quantum logarithmic-space computation assisted by polynomial-size advice.
Edit intent: clarity
Original:  We further give a direct connection of space-bounded quantum computation with quantum advice to quantum finite automata whose transitions are dictated by superpositions of transition tables.
Revised:  We further establish a direct connection of space-bounded quantum computation with quantum advice to quantum finite automata whose transitions are dictated by superpositions of transition tables.
Edit intent: clarity
Original:  We further give a direct connection of space-bounded quantum computation with quantum advice to quantum finite automata whose transitions are dictated by superpositions of transition tables.
Revised:  We further give a direct connection between space-bounded quantum computation with quantum advice to quantum finite automata whose transitions are dictated by superpositions of transition tables.
Edit intent: fluency
Original:  We further give a direct connection of space-bounded quantum computation with quantum advice to quantum finite automata whose transitions are dictated by superpositions of transition tables.
Revised:  We further give a direct connection of space-bounded quantum computation with quantum advice and quantum finite automata whose transitions are dictated by superpositions of transition tables.
Edit intent: fluency
Original:  For two-way quantum finite automata equipped with flexible garbage tapes, we present a close relationship between the nonuniform state complexity of the family of such a polynomial-size quantum finite automata and the parameterized complexity class induced by quantum logarithmic-space  computation assisted by polynomial-size advice.
Revised:  For two-way quantum finite automata equipped with flexible garbage tapes, we show a close relationship between the nonuniform state complexity of the family of such a polynomial-size quantum finite automata and the parameterized complexity class induced by quantum logarithmic-space computation assisted by polynomial-size advice.
Edit intent: clarity
Original:  For two-way quantum finite automata equipped with flexible garbage tapes, we present a close relationship between the nonuniform state complexity of the family of such a polynomial-size quantum finite automata and the parameterized complexity class induced by quantum logarithmic-space  computation assisted by polynomial-size advice.
Revised:  For two-way quantum finite automata equipped with flexible garbage tapes, we present a close relationship between the nonuniform state complexity of the family of such polynomial-size quantum finite automata and the parameterized complexity class induced by quantum logarithmic-space computation assisted by polynomial-size advice.
Edit intent: fluency
Original:  For two-way quantum finite automata equipped with flexible garbage tapes, we present a close relationship between the nonuniform state complexity of the family of such a polynomial-size quantum finite automata and the parameterized complexity class induced by quantum logarithmic-space  computation assisted by polynomial-size advice.
Revised:  For two-way quantum finite automata equipped with flexible garbage tapes, we present a close relationship between the nonuniform state complexity of the family of such a polynomial-size quantum finite automata and the parameterized complexity class induced by logarithmic-space computation assisted by polynomial-size advice.
Edit intent: clarity
Original:  Our main object of study is \| \pi_n - \pi_n\|, where \pi_n and \pi_n are the stationarity distributions of the original and perturbed chains and \| \cdot \| denotes total variation.
Revised:  Our main object of study is \| \pi_n - \pi_n\|, where \pi_n and \pi_n are the stationary distributions of the original and perturbed chains and \| \cdot \| denotes total variation.
Edit intent: fluency
Original: Given a lazy, reversible Markov chain with n states and transition matrix P_n , a distribution \sigma_n over the states, and some \alpha_n \in (0  , 1), we consider restart perturbations, which take the following form: with probability 1-\alpha_n, sample the next state from P_n ;
Revised: Given a reversible Markov chain with n states and transition matrix P_n , a distribution \sigma_n over the states, and some \alpha_n \in (0 , 1), we consider restart perturbations, which take the following form: with probability 1-\alpha_n, sample the next state from P_n ;
Edit intent: clarity
Original: Given a lazy, reversible Markov chain with n states and transition matrix P_n , a distribution \sigma_n over the states, and some \alpha_n \in (0  , 1), we consider restart perturbations, which take the following form: with probability 1-\alpha_n, sample the next state from P_n ;
Revised: Given a lazy, reversible Markov chain P_n on n states, and some \alpha_n \in (0 , 1), we consider restart perturbations, which take the following form: with probability 1-\alpha_n, sample the next state from P_n ;
Edit intent: clarity
Original: Given a lazy, reversible Markov chain with n states and transition matrix P_n , a distribution \sigma_n over the states, and some \alpha_n \in (0  , 1), we consider restart perturbations, which take the following form: with probability 1-\alpha_n, sample the next state from P_n ;
Revised: Given a lazy, reversible Markov chain with n states and transition matrix P_n , a distribution \sigma_n over the states, and another chain , 1), we consider restart perturbations, which take the following form: with probability 1-\alpha_n, sample the next state from P_n ;
Edit intent: clarity
Original:  Our main object of study is \| \pi_n -%DIFDELCMD < \pi%%% _n\|, where \pi_n and%DIFDELCMD < \pi%%% _n are the stationary distributions of the original and perturbed chains and \| \cdot \| denotes total variation.
Revised:  Our main object of study is \| %DIFDELCMD < \pi%%% _n\|, where \pi_n and%DIFDELCMD < \pi%%% _n are the stationary distributions of the original and perturbed chains and \| \cdot \| denotes total variation.
Edit intent: coherence
Original:  Our main object of study is \| \pi_n -%DIFDELCMD < \pi%%% _n\|, where \pi_n and%DIFDELCMD < \pi%%% _n are the stationary distributions of the original and perturbed chains and \| \cdot \| denotes total variation.
Revised:  Our main object of study is \| \pi_n -%DIFDELCMD < \pi%%% %DIFDELCMD < \pi%%% _n are the stationary distributions of the original and perturbed chains and \| \cdot \| denotes total variation.
Edit intent: coherence
Original:  Our first result characterizes \| \pi_n - \pi_n \| in terms of the \epsilon-mixing times t_{mix^{(n)}(\epsilon) of the P_n chain, assuming these mixing times exhibit cutoff.
Revised:  Our first result characterizes \| \pi_n - \pi_n \| ^{(n)}(\epsilon) of the P_n chain, assuming these mixing times exhibit cutoff.
Edit intent: clarity
Original:  and if \alpha_n t_{\textrm{mix}^{(n)}(\epsilon) \rightarrow c \in (}  0, \infty), then \limsup_{n \rightarrow \infty \| \pi_n - \tilde{\pi}_n \| \leq 1 - e^{-c\tilde{P} " trichotomies " have appeared in several result results;
Revised:  and if \alpha_n t_{\textrm{mix}^{(n)}(\epsilon) \rightarrow c \in (} 0, \infty), then \limsup_{n \rightarrow \infty \| \pi_n - \tilde{\pi}_n \| \leq 1 - e^{-c\tilde{P}_n " trichotomies " have appeared in several result results;
Edit intent: fluency
Original:  Our second result shows the weaker notion of pre-cutoff is (almost) equivalent to a certain notion of "sensitivity to perturbation " , in the sense that \| \pi_n -%DIFDELCMD < \tilde{\pi}%%% _n \| \rightarrow 1 for certain perturbations.
Revised:  Our second result shows the weaker notion of pre-cutoff is (almost) equivalent to a notion of "sensitivity to perturbation " , in the sense that \| \pi_n -%DIFDELCMD < \tilde{\pi}%%% _n \| \rightarrow 1 for certain perturbations.
Edit intent: clarity
Original:  Our second result shows the weaker notion of pre-cutoff is (almost) equivalent to a certain notion of "sensitivity to perturbation " , in the sense that \| \pi_n -%DIFDELCMD < \tilde{\pi}%%% _n \| \rightarrow 1 for certain perturbations.
Revised:  Our second result shows the weaker notion of pre-cutoff is (almost) equivalent to a certain notion of "sensitivity to restart perturbations, " , in the sense that \| \pi_n -%DIFDELCMD < \tilde{\pi}%%% _n \| \rightarrow 1 for certain perturbations.
Edit intent: fluency
Original:  Our second result shows the weaker notion of pre-cutoff is (almost) equivalent to a certain notion of "sensitivity to perturbation " , in the sense that \| \pi_n -%DIFDELCMD < \tilde{\pi}%%% _n \| \rightarrow 1 for certain perturbations.
Revised:  Our second result shows the weaker notion of pre-cutoff is (almost) equivalent to a certain notion of "sensitivity to perturbation " %DIFDELCMD < \tilde{\pi}%%% _n \| \rightarrow 1 for certain perturbations.
Edit intent: coherence
Original: Graph Edit Distance (GED) measures the dissimilarity between two graphs as the minimal cost of a sequence of elementary operations transforming one graph into another.
Revised: The graph edit distance (GED) measures the dissimilarity between two graphs as the minimal cost of a sequence of elementary operations transforming one graph into another.
Edit intent: clarity
Original: Surprise-based learning allows agents to adapt quickly in non-stationary stochastic environments .
Revised: Surprise-based learning allows agents to rapidly adapt to non-stationary stochastic environments .
Edit intent: clarity
Original:  In this work we show that exact Bayesian inference gives naturally rise to a surprise-modulated trade-off between forgetting and integrating the new observations with the current belief.
Revised:  We show that exact Bayesian inference gives naturally rise to a surprise-modulated trade-off between forgetting and integrating the new observations with the current belief.
Edit intent: clarity
Original:  Empirical results show that these filters estimate parameters better than alternative approximate approaches and reach comparative levels of performance  to computationally more expensive algorithms.
Revised:  Empirical results show that these filters estimate parameters better than alternative approximate approaches and reach levels of performance to computationally more expensive algorithms.
Edit intent: clarity
Original:  Empirical results show that these filters estimate parameters better than alternative approximate approaches and reach comparative levels of performance  to computationally more expensive algorithms.
Revised:  Empirical results show that these filters estimate parameters better than alternative approximate approaches and reach comparative levels of performance comparable to computationally more expensive algorithms.
Edit intent: clarity
Original:  The  theoretical insight of casting various approaches under the same interpretation of surprise-based learning, as well as the proposed filters, may find useful applications in reinforcement learning in non-stationary environments and in the analysis of animal and human behavior  .
Revised:  The theoretical insight of casting various approaches under the same interpretation of surprise-based learning, as well as the proposed online algorithms, may be applied to the analysis of animal and human behavior .
Edit intent: clarity
Original: Surprise-based learning allows agents to rapidly adapt to non-stationary stochastic environments characterized by stationary periods separated by sudden changes.
Revised: Surprise-based learning allows agents to rapidly adapt to non-stationary stochastic environments characterized by sudden changes.
Edit intent: clarity
Original:  The modulation depends on a probability ratio, called the "Bayes Factor Surprise"  that tests the prior belief against the current belief.
Revised:  The modulation depends on a probability ratio, which we call "Bayes Factor Surprise" that tests the prior belief against the current belief.
Edit intent: coherence
Original:  The modulation depends on a probability ratio, called the "Bayes Factor Surprise"  that tests the prior belief against the current belief.
Revised:  The modulation depends on a probability ratio, called the "Bayes Factor Surprise" , that tests the prior belief against the current belief.
Edit intent: fluency
Original:  In two hypothetical experiments, we make testable predictions for physiological or behavioral indicators that dissociate the Bayes Factor Surprise from Shannon Surprise.
Revised:  In two hypothetical experiments, we make testable predictions for physiological indicators that dissociate the Bayes Factor Surprise from Shannon Surprise.
Edit intent: clarity
Original: We give the first fully dynamic algorithm which maintains a ( 1+ \epsilon)-approximate densest subgraph in worst-case time poly(\log n, \epsilon^{-1}) per update with high probability .
Revised: We give the first fully dynamic algorithm which maintains a ( 1+ \epsilon)-approximate densest subgraph in worst-case time poly(\log n, \epsilon^{-1}) per update .
Edit intent: clarity
Original:   Our result improves upon the previous best approximation factor of (4+\epsilon) \left({4} - \epsilon}\right) for fully dynamic densest subgraph obtained by [ Bhattacharya-Henzinger-Nanongkai-Tsourakakis , STOC `15].
Revised:  Our result improves upon the previous best approximation factor of \left({4} - \epsilon}\right) for fully dynamic densest subgraph obtained by [ Bhattacharya-Henzinger-Nanongkai-Tsourakakis , STOC `15].
Edit intent: clarity
Original:   Our result improves upon the previous best approximation factor of (4+\epsilon) \left({4} - \epsilon}\right) for fully dynamic densest subgraph obtained by [ Bhattacharya-Henzinger-Nanongkai-Tsourakakis , STOC `15].
Revised:  Our result improves upon the previous best approximation factor of (4+\epsilon) \left({4} - \epsilon}\right) for fully dynamic densest subgraph [ Bhattacharya-Henzinger-Nanongkai-Tsourakakis , STOC `15].
Edit intent: clarity
Original:  Our algorithm combines the uniform sparsification technique used in [ Mitzenmacher-Pachocki-Peng-Tsourakakis-Xu, KDD`15 ] and McGregor-Tench-Vorotnikova-Vu, MFCS`15%DIFDELCMD < ] %%% along with an augmenting path-like dual adjustment technique to maintain an approximate solution efficiently .
Revised:  Our algorithm combines the uniform sparsification technique used in [ Mitzenmacher-Pachocki-Peng-Tsourakakis-Xu, KDD`15 ] McGregor-Tench-Vorotnikova-Vu, MFCS`15%DIFDELCMD < ] %%% along with an augmenting path-like dual adjustment technique to maintain an approximate solution efficiently .
Edit intent: coherence
Original:  Our algorithm combines the uniform sparsification technique used in [ Mitzenmacher-Pachocki-Peng-Tsourakakis-Xu, KDD`15 ] and McGregor-Tench-Vorotnikova-Vu, MFCS`15%DIFDELCMD < ] %%% along with an augmenting path-like dual adjustment technique to maintain an approximate solution efficiently .
Revised:  Our algorithm combines the uniform sparsification technique used in [ Mitzenmacher-Pachocki-Peng-Tsourakakis-Xu, KDD`15 ] and %DIFDELCMD < ] %%% along with an augmenting path-like dual adjustment technique to maintain an approximate solution efficiently .
Edit intent: coherence
Original:  Fog computing makes it possible to fulfill real-time requirements of applications by bringing more processing, storage, and control power geographically closer to edge devices .
Revised:  Fog computing makes it possible to fulfill real-time requirements of applications by bringing more processing, storage, and control power geographically closer to end-devices .
Edit intent: clarity