wanyu/IteraTeR_full_sent huggingface dataset:
Original:  There phases are identified: an inactive phase in which mean time to extinction T  scales logarithmically with the initial population size , a temporal Griffiths phase where T \sim N^q , where N is the carrying capacity, and an exponential phase with T \sim exp(\alpha N).
Revised:  There phases are identified: an inactive phase in which mean time to extinction T is independent of the carrying capacity N, and scales logarithmically with the initial population size , a temporal Griffiths phase where T \sim N^q , where N is the carrying capacity, and an exponential phase with T \sim exp(\alpha N).
Edit intent: meaning-changed
Original:  There phases are identified: an inactive phase in which mean time to extinction T  scales logarithmically with the initial population size , a temporal Griffiths phase where T \sim N^q , where N is the carrying capacity, and an exponential phase with T \sim exp(\alpha N).
Revised:  There phases are identified: an inactive phase in which mean time to extinction T scales logarithmically with the initial population size . In the power-law phase T \sim N^q , where N is the carrying capacity, and an exponential phase with T \sim exp(\alpha N).
Edit intent: meaning-changed
Original:  There phases are identified: an inactive phase in which mean time to extinction T  scales logarithmically with the initial population size , a temporal Griffiths phase where T \sim N^q , where N is the carrying capacity, and an exponential phase with T \sim exp(\alpha N).
Revised:  There phases are identified: an inactive phase in which mean time to extinction T scales logarithmically with the initial population size , a temporal Griffiths phase where T \sim N^q and the exponential phase T \sim exp(\alpha N).
Edit intent: clarity
Original: We show that coherent risk measures are ineffective in curbing the behaviour of investors with limited liability  if the market admits statistical arbitrage opportunities which we term \rho-arbitrage for a risk measure \rho.
Revised: We show that coherent risk measures are ineffective in curbing the behaviour of investors with limited liability or excessive tail-risk seeking behaviour if the market admits statistical arbitrage opportunities which we term \rho-arbitrage for a risk measure \rho.
Edit intent: meaning-changed
Original:  Robust motifs are graphs associated to threshold-linear networks (TLNs) for which the structure of fixed points  is independent of the choice of connectivity matrix W . In this work we describe infinite families of robust motifs, and use them to completely characterize all robust motifs for networks of size n \leq 5.
Revised: To any inhibition-dominated threshold-linear network (TLN) we can associate a directed graph that captures the pattern of strong and weak inhibition between neurons. Robust motifs are graphs associated to threshold-linear networks (TLNs) for which the structure of fixed points is independent of the choice of connectivity matrix W . In this work we describe infinite families of robust motifs, and use them to completely characterize all robust motifs for networks of size n \leq 5.
Edit intent: meaning-changed
Original:  Robust motifs are graphs associated to threshold-linear networks (TLNs) for which the structure of fixed points  is independent of the choice of connectivity matrix W . In this work we describe infinite families of robust motifs, and use them to completely characterize all robust motifs for networks of size n \leq 5.
Revised:  Robust motifs are graphs for which the structure of fixed points is independent of the choice of connectivity matrix W . In this work we describe infinite families of robust motifs, and use them to completely characterize all robust motifs for networks of size n \leq 5.
Edit intent: clarity
Original:  Robust motifs are graphs associated to threshold-linear networks (TLNs) for which the structure of fixed points  is independent of the choice of connectivity matrix W . In this work we describe infinite families of robust motifs, and use them to completely characterize all robust motifs for networks of size n \leq 5.
Revised:  Robust motifs are graphs associated to threshold-linear networks (TLNs) for which the structure of fixed points in the network is independent of the choice of connectivity matrix W . In this work we describe infinite families of robust motifs, and use them to completely characterize all robust motifs for networks of size n \leq 5.
Edit intent: clarity
Original:  Robust motifs are graphs associated to threshold-linear networks (TLNs) for which the structure of fixed points  is independent of the choice of connectivity matrix W . In this work we describe infinite families of robust motifs, and use them to completely characterize all robust motifs for networks of size n \leq 5. These graph structures tightly constrain the dynamics of the associated TLNs, making them ideal candidates for constructing network architectures whose dynamics are robust despite allowing great flexibility in the choice of W .
Revised:  Robust motifs are graphs associated to threshold-linear networks (TLNs) for which the structure of fixed points is independent of the choice of connectivity matrix W , and whose dynamics are thus greatly constrained. This makes them ideal building blocks for constructing larger networks whose behaviors are robust to changes in connection strengths. In contrast, flexible motifs correspond to networks with multiple dynamic regimes. In this work, we give a purely graphical characterization of both flexible and robust motifs of any size. We find that all but a few robust motifs fall into two infinite families of graphs with simple feedforward architectures .
Edit intent: meaning-changed
Original:  For unit-length intervals, we obtain a (2+\epsilon)-approximation to \alpha and \beta in poly %DIFDELCMD < \left(%%% \frac{\log(n){\epsilon}}%DIFDELCMD < \right) %%% {\epsilon}) } space.
Revised:  For unit-length intervals, we obtain a (2+\epsilon)-approximation to \alpha and \beta in poly %DIFDELCMD < \left(%%% {\epsilon}}%DIFDELCMD < \right) %%% {\epsilon}) } space.
Edit intent: meaning-changed
Original:  For unit-length intervals, we obtain a (2+\epsilon)-approximation to \alpha and \beta in poly %DIFDELCMD < \left(%%% \frac{\log(n){\epsilon}}%DIFDELCMD < \right) %%% {\epsilon}) } space.
Revised:  For unit-length intervals, we obtain a (2+\epsilon)-approximation to \alpha and \beta in poly %DIFDELCMD < \left(%%% \frac{\log(n){\epsilon}}%DIFDELCMD < \right) %%% (\frac{\log(n){\epsilon}) } space.
Edit intent: coherence
Original:  For arbitrary-length intervals, we show any c-approximation to \alpha , and thus also \beta , requires \Omega ] \left( \frac{n^{1/c}{2^c}}%DIFDELCMD < \right) %%% space.
Revised:  Combined with the 3/2-approximation for insertion-only streams by Cabello and Perez-Lanterno ] \left( \frac{n^{1/c}{2^c}}%DIFDELCMD < \right) %%% space.
Edit intent: meaning-changed
Original:  For arbitrary-length intervals, we show any c-approximation to \alpha , and thus also \beta , requires \Omega ] \left( \frac{n^{1/c}{2^c}}%DIFDELCMD < \right) %%% space.
Revised:  For arbitrary-length intervals, we show any c-approximation to \alpha , and thus also \beta , requires \Omega CP15] \left( \frac{n^{1/c}{2^c}}%DIFDELCMD < \right) %%% space.
Edit intent: meaning-changed
Original:  For arbitrary-length intervals, we show any c-approximation to \alpha , and thus also \beta , requires \Omega ] \left( \frac{n^{1/c}{2^c}}%DIFDELCMD < \right) %%% space.
Revised:  For arbitrary-length intervals, we show any c-approximation to \alpha , and thus also \beta , requires \Omega ], our result implies a separation between the insertion-only and turnstile model. For unit-radius disks, we obtain a \left( \frac{n^{1/c}{2^c}}%DIFDELCMD < \right) %%% space.
Edit intent: meaning-changed
Original:  For arbitrary-length intervals, we show any c-approximation to \alpha , and thus also \beta , requires \Omega ] \left( \frac{n^{1/c}{2^c}}%DIFDELCMD < \right) %%% space.
Revised:  For arbitrary-length intervals, we show any c-approximation to \alpha , and thus also \beta , requires \Omega ] \left( }{2^c}}%DIFDELCMD < \right) %%% space.
Edit intent: meaning-changed
Original:  For arbitrary-length intervals, we show any c-approximation to \alpha , and thus also \beta , requires \Omega ] \left( \frac{n^{1/c}{2^c}}%DIFDELCMD < \right) %%% space. To this end, we introduce a new communication problem and lower bound its information complexity. In light of the lower bound we}{\pi}}\right) provide algorithms for estimating \alpha for arbitrary-length intervals under a bounded intersection assumption .
Revised:  For arbitrary-length intervals, we show any c-approximation to \alpha , and thus also \beta , requires \Omega ] \left( \frac{n^{1/c}{2^c}}%DIFDELCMD < \right) %%% \frac{8\sqrt{3}{\pi}}\right) provide algorithms for estimating \alpha for arbitrary-length intervals under a bounded intersection assumption .
Edit intent: meaning-changed
Original:  In light of the lower bound we}{\pi}}\right) provide algorithms for estimating \alpha for arbitrary-length intervals under a bounded intersection assumption .
Revised:  In light of the lower bound we}{\pi}}\right)-approximation to \alpha and \beta in poly(\log(n), \epsilon^{-1 provide algorithms for estimating \alpha for arbitrary-length intervals under a bounded intersection assumption .
Edit intent: meaning-changed
Original:  In light of the lower bound we}{\pi}}\right) provide algorithms for estimating \alpha for arbitrary-length intervals under a bounded intersection assumption . We also study the parameterized space complexity of estimating \alpha and \beta, where the parameter is the ratio of maximum to minimum interval length .
Revised:  In light of the lower bound we}{\pi}}\right) provide algorithms for estimating \alpha for arbitrary-length intervals under a bounded intersection assumption and study the parameterized space complexity of estimating \alpha and \beta, where the parameter is the ratio of maximum to minimum interval length .
Edit intent: coherence
Original:  We also study the parameterized space complexity of estimating \alpha and \beta, where the parameter is the ratio of maximum to minimum interval length . For unit-radius disks, we obtain a%DIFDELCMD < \left(%%% \frac{8\sqrt{3}{\pi}}%DIFDELCMD < \right)%%% -approximation to \alpha and \beta in\textrm{poly}%DIFAUXCMD %DIFDELCMD < \left(%%% \frac{\log(n){\epsilon}}%DIFDELCMD < \right) %%% space, which is closely related to the hexagonal circle packing constant .
Revised:  We also study the parameterized space complexity of estimating \alpha and \beta, where the parameter is the ratio of maximum to minimum interval length %DIFDELCMD < \left(%%% \frac{8\sqrt{3}{\pi}}%DIFDELCMD < \right)%%% -approximation to \alpha and \beta in\textrm{poly}%DIFAUXCMD %DIFDELCMD < \left(%%% \frac{\log(n){\epsilon}}%DIFDELCMD < \right) %%% space, which is closely related to the hexagonal circle packing constant .
Edit intent: coherence
Original:  For unit-radius disks, we obtain a%DIFDELCMD < \left(%%% \frac{8\sqrt{3}{\pi}}%DIFDELCMD < \right)%%% -approximation to \alpha and \beta in\textrm{poly}%DIFAUXCMD %DIFDELCMD < \left(%%% \frac{\log(n){\epsilon}}%DIFDELCMD < \right) %%% space, which is closely related to the hexagonal circle packing constant .
Revised:  For unit-radius disks, we obtain a%DIFDELCMD < \left(%%% }{\pi}}%DIFDELCMD < \right)%%% -approximation to \alpha and \beta in\textrm{poly}%DIFAUXCMD %DIFDELCMD < \left(%%% \frac{\log(n){\epsilon}}%DIFDELCMD < \right) %%% space, which is closely related to the hexagonal circle packing constant .
Edit intent: meaning-changed
Original:  For unit-radius disks, we obtain a%DIFDELCMD < \left(%%% \frac{8\sqrt{3}{\pi}}%DIFDELCMD < \right)%%% -approximation to \alpha and \beta in\textrm{poly}%DIFAUXCMD %DIFDELCMD < \left(%%% \frac{\log(n){\epsilon}}%DIFDELCMD < \right) %%% space, which is closely related to the hexagonal circle packing constant .
Revised:  For unit-radius disks, we obtain a%DIFDELCMD < \left(%%% \frac{8\sqrt{3}{\pi}}%DIFDELCMD < \right)%%% \textrm{poly}%DIFAUXCMD %DIFDELCMD < \left(%%% \frac{\log(n){\epsilon}}%DIFDELCMD < \right) %%% space, which is closely related to the hexagonal circle packing constant .
Edit intent: meaning-changed
Original:  For unit-radius disks, we obtain a%DIFDELCMD < \left(%%% \frac{8\sqrt{3}{\pi}}%DIFDELCMD < \right)%%% -approximation to \alpha and \beta in\textrm{poly}%DIFAUXCMD %DIFDELCMD < \left(%%% \frac{\log(n){\epsilon}}%DIFDELCMD < \right) %%% space, which is closely related to the hexagonal circle packing constant .
Revised:  For unit-radius disks, we obtain a%DIFDELCMD < \left(%%% \frac{8\sqrt{3}{\pi}}%DIFDELCMD < \right)%%% -approximation to \alpha and \beta in\textrm{}%DIFAUXCMD %DIFDELCMD < \left(%%% \frac{\log(n){\epsilon}}%DIFDELCMD < \right) %%% space, which is closely related to the hexagonal circle packing constant .
Edit intent: fluency
Original:  For unit-radius disks, we obtain a%DIFDELCMD < \left(%%% \frac{8\sqrt{3}{\pi}}%DIFDELCMD < \right)%%% -approximation to \alpha and \beta in\textrm{poly}%DIFAUXCMD %DIFDELCMD < \left(%%% \frac{\log(n){\epsilon}}%DIFDELCMD < \right) %%% space, which is closely related to the hexagonal circle packing constant .
Revised:  For unit-radius disks, we obtain a%DIFDELCMD < \left(%%% \frac{8\sqrt{3}{\pi}}%DIFDELCMD < \right)%%% -approximation to \alpha and \beta in\textrm{poly}%DIFAUXCMD %DIFDELCMD < \left(%%% {\epsilon}}%DIFDELCMD < \right) %%% space, which is closely related to the hexagonal circle packing constant .
Edit intent: meaning-changed
Original:  For unit-radius disks, we obtain a%DIFDELCMD < \left(%%% \frac{8\sqrt{3}{\pi}}%DIFDELCMD < \right)%%% -approximation to \alpha and \beta in\textrm{poly}%DIFAUXCMD %DIFDELCMD < \left(%%% \frac{\log(n){\epsilon}}%DIFDELCMD < \right) %%% space, which is closely related to the hexagonal circle packing constant .
Revised:  For unit-radius disks, we obtain a%DIFDELCMD < \left(%%% \frac{8\sqrt{3}{\pi}}%DIFDELCMD < \right)%%% -approximation to \alpha and \beta in\textrm{poly}%DIFAUXCMD %DIFDELCMD < \left(%%% \frac{\log(n){\epsilon}}%DIFDELCMD < \right) %%% .
Edit intent: meaning-changed
Original:  To obtain a test which retains the appropriate size after the variable selection done by the lasso, we propose a post-double-selection procedure to partial out the effects of the variables not of interest .
Revised:  To obtain a test which retains the appropriate size after the variable selection done by the lasso, we propose a post-double-selection procedure to partial out effects of nuisance variables and establish its uniform asymptotic validity .
Edit intent: meaning-changed
Original:  The test performs well under different data generating processes, even when the underlying model is not very sparse. Additionally, we investigate two empirical applications : the money-income causality relation using a large macroeconomic dataset and networks of realized volatilities of a set of 49 stocks. In both applications we find evidences that the causal relationship becomes much clearer if a high-dimensional VAR is considered compared to a standard low-dimensional one .
Revised:  The test performs well under different data generating processes, even without sparsity. In two applications on money and income and on volatility spillovers we find evidence that causal relationships become clearer in high-dimensional VAR is considered compared to a standard low-dimensional one .
Edit intent: clarity
Original: Empirical demand models used for counterfactual predictions and welfare analysis must be rationalizable , i.e. theoretically consistent with utility maximization by heterogeneous consumers.
Revised: An important goal of empirical demand analysis is choice and welfare prediction on counterfactual budget sets arising from potential policy-interventions. Such predictions are more credible when made without arbitrary functional-form/distributional assumptions, and instead based solely on economic rationality , i.e. theoretically consistent with utility maximization by heterogeneous consumers.
Edit intent: meaning-changed
Original: Empirical demand models used for counterfactual predictions and welfare analysis must be rationalizable , i.e. theoretically consistent with utility maximization by heterogeneous consumers.
Revised: Empirical demand models used for counterfactual predictions and welfare analysis must be rationalizable , i.e. theoretically consistent with utility maximization by a heterogeneous population. This paper investigates nonparametric economic rationality in the empirically important context of binary choice.
Edit intent: meaning-changed
Original: In multinomial choice settings with additive heterogeneity, Daly-Zachary (1978) and Armstrong-Vickers (2015) provided closed-form conditions, under which choice probability functions can be rationalized via random utility models . A key condition is Slutsky symmetry.
Revised: McFadden's Random-Utility Model of multinomial choice has long been the workhorse of applied research. We establish shape-restrictions under which multinomial choice-probability functions can be rationalized via random utility models . A key condition is Slutsky symmetry.
Edit intent: meaning-changed
Original: In multinomial choice settings with additive heterogeneity, Daly-Zachary (1978) and Armstrong-Vickers (2015) provided closed-form conditions, under which choice probability functions can be rationalized via random utility models . A key condition is Slutsky symmetry. We first show that in the multinomial context, Daly-Zachary's Slutsky symmetry is equivalent to absence of income-effects.
Revised: In multinomial choice settings with additive heterogeneity, Daly-Zachary (1978) and Armstrong-Vickers (2015) provided closed-form conditions, under which choice probability functions can be rationalized via random-utility models with nonparametric heterogeneity and general income-effects.
Edit intent: meaning-changed
Original:  Next, for general multinomial choice that allows for income-effects, we provide global shape restrictions on choice probability functions, which are shown to be sufficient for rationalizability. Finally, we outline nonparametric identification of preference distributions using these results .
Revised:  Next, for general multinomial choice that allows for income-effects, we provide global shape restrictions on choice probability functions, which are shown to be necessary and sufficient for the canonical Additive Random Utility Model (ARUM). The sufficiency-proof is constructive, and facilitates nonparametric identification of preference distributions using these results .
Edit intent: meaning-changed
Original:  When combined with an additional restriction, the above conditions are shown to be necessary and sufficient for the canonical Additive Random Utility Model (ARUM) . The sufficiency-proof is constructive, and facilitates nonparametric identification of preference-distributions  .
Revised:  When combined with an additional restriction, the above conditions are equivalent to the canonical Additive Random Utility Model (ARUM) . The sufficiency-proof is constructive, and facilitates nonparametric identification of preference-distributions .
Edit intent: clarity
Original:  When combined with an additional restriction, the above conditions are shown to be necessary and sufficient for the canonical Additive Random Utility Model (ARUM) . The sufficiency-proof is constructive, and facilitates nonparametric identification of preference-distributions  .
Revised:  When combined with an additional restriction, the above conditions are shown to be necessary and sufficient for the canonical Additive Random Utility Model . The sufficiency-proof is constructive, and facilitates nonparametric identification of preference-distributions .
Edit intent: clarity
Original:  When combined with an additional restriction, the above conditions are shown to be necessary and sufficient for the canonical Additive Random Utility Model (ARUM) . The sufficiency-proof is constructive, and facilitates nonparametric identification of preference-distributions  .
Revised:  When combined with an additional restriction, the above conditions are shown to be necessary and sufficient for the canonical Additive Random Utility Model (ARUM) . The sufficiency-proof is constructive, and facilitates nonparametric identification of preference-distributions without requiring identification-at-infinity type arguments .
Edit intent: meaning-changed
Original:  A corollary establishes that Slutsky-symmetry, a key condition for previous rationalizability results (Daly-Zachary 1978, Armstrong-Vickers 2015), is equivalent to absence of income-effects.
Revised:  A corollary shows that Slutsky-symmetry, a key condition for previous rationalizability results (Daly-Zachary 1978, Armstrong-Vickers 2015), is equivalent to absence of income-effects.
Edit intent: clarity
Original:  That is, the set D satisfies the condition that |N[v]\cap D|\geq 1 for each v\in V, where N[v] is the closed neighborhood of v. In this paper, we study two variants of the classical dominating set problem: k-tuple dominating set (k-DS) problem and Liar's dominating set (LDS) problem, and obtain several algorithmic and hardness results.
Revised:  That is, the set D satisfies the condition that |N[v]\cap D|\geq 1 for each v\in V, where N[v] is the closed neighborhood of v. In this paper, we study two variants of the classical dominating set problem: -tuple dominating set (k-DS) problem and Liar's dominating set (LDS) problem, and obtain several algorithmic and hardness results.
Edit intent: fluency
Original:  On the hardness side, we show a \Omega (n^2) bits lower bound for the space complexity of any (randomized) streaming algorithm for Liar's dominating set problem as well as for the k-tuple dominating set problem.
Revised:  On the hardness side, we show a \Omega (n^2) bits lower bound for the space complexity of any (randomized) streaming algorithm for Liar's dominating set problem as well as for the -tuple dominating set problem.
Edit intent: clarity
Original:  Even though antifragile dynamics are found in various real-world complex systems where multiple subsystems interact with each other, the attribute has not been quantitatively explored yet in those complex systems which can be regarded as multilayer networks.
Revised:  Even though antifragile dynamics is found in various real-world complex systems where multiple subsystems interact with each other, the attribute has not been quantitatively explored yet in those complex systems which can be regarded as multilayer networks.
Edit intent: fluency
Original: A large variety of methods has been proposed for automatic seizure detection in EEG signals. Those achieving maximal performance are based on machine-learning techniques, which require long training sessions with large labelled databases, and produce a verdict with no intuitive justification. As an alternative, we here explore an unsupervised algorithm applicable to intra-cranial EEG recordings that requires good sampling of the non-ictal periods , but imposes no demands on the amount of data during ictal activity.
Revised: The amount of power in different frequency bands of the electroencephalogram (EEG) carries information about the behavioral state of a subject. Hence, neurologists treating epileptic patients monitor the temporal evolution of the different bands. We propose a covariance-based method to detect and characterize epileptic seizures operating on the band-filtered EEG signal. The algorithm is unsupervised, and performs a principal component analysis of intra-cranial EEG recordings that requires good sampling of the non-ictal periods , but imposes no demands on the amount of data during ictal activity.
Edit intent: meaning-changed