wanyu/IteraTeR_full_sent huggingface dataset:
Original:  that are sums of sparse SOS matrices , each of which is zero outside a small principal submatrix is not compact or does not satisfy the Archimedean condition, we obtain a similar decomposition for (x_1^2 + \ldots + x_n^2)^\nu P(x) with some integer \nu\geq 0 when P and g_1,\ldots,g_m are homogeneous of even degree} . Using these decomposition results, we obtain sparse SOS representation theorems for polynomials that are quadratic and correlatively sparse in a subset of variables . We also obtain new convergent hierarchies of sparsity-exploiting SOS reformulations to convex optimization problems with large and sparse polynomial matrix inequalities.
Revised:  that are sums of sparse SOS matrices , each of which is zero outside a small principal submatrix is not compact or does not satisfy the Archimedean condition, we obtain a similar decomposition for (x_1^2 + \ldots + x_n^2)^\nu P(x) with some integer \nu\geq 0 when P and g_1,\ldots,g_m are homogeneous of even degree} . Using these decomposition results, we obtain sparse SOS representation theorems for polynomials that are quadratic and correlatively sparse in a subset of variables , and we construct new convergent hierarchies of sparsity-exploiting SOS reformulations to convex optimization problems with large and sparse polynomial matrix inequalities.
Edit intent: clarity
Original: In this work, different transmission modes of the SARS-CoV-2 virus  and their role in determining the evolution of the Covid-19 pandemic are analyzed  . Probability of infection caused by inhaling infectious droplets (initial, ejection diameters between 0.5-750\mu m) and probability of infection by the corresponding desiccated nuclei that mostly encapsulate the virions post droplet evaporation, are  calculated.
Revised: Identifying the relative importance of the different transmission routes of the SARS-CoV-2 virus and their role in determining the evolution of the Covid-19 pandemic are analyzed . Probability of infection caused by inhaling infectious droplets (initial, ejection diameters between 0.5-750\mu m) and probability of infection by the corresponding desiccated nuclei that mostly encapsulate the virions post droplet evaporation, are calculated.
Edit intent: clarity
Original: In this work, different transmission modes of the SARS-CoV-2 virus  and their role in determining the evolution of the Covid-19 pandemic are analyzed  . Probability of infection caused by inhaling infectious droplets (initial, ejection diameters between 0.5-750\mu m) and probability of infection by the corresponding desiccated nuclei that mostly encapsulate the virions post droplet evaporation, are  calculated.
Revised: In this work, different transmission modes of the SARS-CoV-2 virus is an urgent research priority. To that end, the different transmission routes, and their role in determining the evolution of the Covid-19 pandemic are analyzed . Probability of infection caused by inhaling infectious droplets (initial, ejection diameters between 0.5-750\mu m) and probability of infection by the corresponding desiccated nuclei that mostly encapsulate the virions post droplet evaporation, are calculated.
Edit intent: coherence
Original: In this work, different transmission modes of the SARS-CoV-2 virus  and their role in determining the evolution of the Covid-19 pandemic are analyzed  . Probability of infection caused by inhaling infectious droplets (initial, ejection diameters between 0.5-750\mu m) and probability of infection by the corresponding desiccated nuclei that mostly encapsulate the virions post droplet evaporation, are  calculated.
Revised: In this work, different transmission modes of the SARS-CoV-2 virus and their role in determining the evolution of the Covid-19 pandemic are analyzed in this work . Probability of infection caused by inhaling infectious droplets (initial, ejection diameters between 0.5-750\mu m) and probability of infection by the corresponding desiccated nuclei that mostly encapsulate the virions post droplet evaporation, are calculated.
Edit intent: coherence
Original: In this work, different transmission modes of the SARS-CoV-2 virus  and their role in determining the evolution of the Covid-19 pandemic are analyzed  . Probability of infection caused by inhaling infectious droplets (initial, ejection diameters between 0.5-750\mu m) and probability of infection by the corresponding desiccated nuclei that mostly encapsulate the virions post droplet evaporation, are  calculated.
Revised: In this work, different transmission modes of the SARS-CoV-2 virus and their role in determining the evolution of the Covid-19 pandemic are analyzed . Probability of infection caused by inhaling virus-laden droplets (initial, ejection diameters between 0.5-750\mu m) and probability of infection by the corresponding desiccated nuclei that mostly encapsulate the virions post droplet evaporation, are calculated.
Edit intent: clarity
Original: In this work, different transmission modes of the SARS-CoV-2 virus  and their role in determining the evolution of the Covid-19 pandemic are analyzed  . Probability of infection caused by inhaling infectious droplets (initial, ejection diameters between 0.5-750\mu m) and probability of infection by the corresponding desiccated nuclei that mostly encapsulate the virions post droplet evaporation, are  calculated.
Revised: In this work, different transmission modes of the SARS-CoV-2 virus and their role in determining the evolution of the Covid-19 pandemic are analyzed . Probability of infection caused by inhaling infectious droplets (initial, ejection diameters between 0.5-750\mu m) and the corresponding desiccated nuclei that mostly encapsulate the virions post droplet evaporation, are calculated.
Edit intent: coherence
Original: In this work, different transmission modes of the SARS-CoV-2 virus  and their role in determining the evolution of the Covid-19 pandemic are analyzed  . Probability of infection caused by inhaling infectious droplets (initial, ejection diameters between 0.5-750\mu m) and probability of infection by the corresponding desiccated nuclei that mostly encapsulate the virions post droplet evaporation, are  calculated.
Revised: In this work, different transmission modes of the SARS-CoV-2 virus and their role in determining the evolution of the Covid-19 pandemic are analyzed . Probability of infection caused by inhaling infectious droplets (initial, ejection diameters between 0.5-750\mu m) and probability of infection by the corresponding desiccated nuclei that mostly encapsulate the virions post droplet evaporation, are individually calculated.
Edit intent: clarity
Original:  At typical, air-conditioned yet quiescent , large indoor space, for the average viral loading, and at early times, cough droplets of initial diameter between 10 \mu m and 50 \mu m have the highest infection probability.
Revised:  At typical, air-conditioned yet quiescent indoor space, for the average viral loading, and at early times, cough droplets of initial diameter between 10 \mu m and 50 \mu m have the highest infection probability.
Edit intent: clarity
Original:  At typical, air-conditioned yet quiescent , large indoor space, for the average viral loading, and at early times, cough droplets of initial diameter between 10 \mu m and 50 \mu m have the highest infection probability.
Revised:  At typical, air-conditioned yet quiescent , large indoor space, for average viral loading, and at early times, cough droplets of initial diameter between 10 \mu m and 50 \mu m have the highest infection probability.
Edit intent: fluency
Original:  At typical, air-conditioned yet quiescent , large indoor space, for the average viral loading, and at early times, cough droplets of initial diameter between 10 \mu m and 50 \mu m have the highest infection probability.
Revised:  At typical, air-conditioned yet quiescent , large indoor space, for the average viral loading, cough droplets of initial diameter between 10 \mu m and 50 \mu m have the highest infection probability.
Edit intent: coherence
Original:  At typical, air-conditioned yet quiescent , large indoor space, for the average viral loading, and at early times, cough droplets of initial diameter between 10 \mu m and 50 \mu m have the highest infection probability.
Revised:  At typical, air-conditioned yet quiescent , large indoor space, for the average viral loading, and at early times, cough droplets of initial diameter between 10-50 \mu m have the highest infection probability.
Edit intent: fluency
Original:  While the initially near unity infection probability due to droplets (airborne/ballistic) rapidly decays within the first 25s, the small yet persistent infection probability of airborne desiccated nuclei decays appreciably only by  1000s  . Combined with molecular collision theory adapted to calculate frequency of contact between the susceptible population and the droplet/nuclei cloud, infection probabilities are used to define infection rate constants , ab-initio, leading to a SEIR model .
Revised:  While the initially near unity infection probability due to droplets rapidly decays within the first 25s, the small yet persistent infection probability of airborne desiccated nuclei decays appreciably only by 1000s . Combined with molecular collision theory adapted to calculate frequency of contact between the susceptible population and the droplet/nuclei cloud, infection probabilities are used to define infection rate constants , ab-initio, leading to a SEIR model .
Edit intent: clarity
Original:  While the initially near unity infection probability due to droplets (airborne/ballistic) rapidly decays within the first 25s, the small yet persistent infection probability of airborne desiccated nuclei decays appreciably only by  1000s  . Combined with molecular collision theory adapted to calculate frequency of contact between the susceptible population and the droplet/nuclei cloud, infection probabilities are used to define infection rate constants , ab-initio, leading to a SEIR model .
Revised:  While the initially near unity infection probability due to droplets (airborne/ballistic) rapidly decays within the first 25s, the small yet persistent infection probability of desiccated nuclei decays appreciably only by 1000s . Combined with molecular collision theory adapted to calculate frequency of contact between the susceptible population and the droplet/nuclei cloud, infection probabilities are used to define infection rate constants , ab-initio, leading to a SEIR model .
Edit intent: fluency
Original:  While the initially near unity infection probability due to droplets (airborne/ballistic) rapidly decays within the first 25s, the small yet persistent infection probability of airborne desiccated nuclei decays appreciably only by  1000s  . Combined with molecular collision theory adapted to calculate frequency of contact between the susceptible population and the droplet/nuclei cloud, infection probabilities are used to define infection rate constants , ab-initio, leading to a SEIR model .
Revised:  While the initially near unity infection probability due to droplets (airborne/ballistic) rapidly decays within the first 25s, the small yet persistent infection probability of airborne desiccated nuclei decays appreciably only by \mathcal{O 1000s . Combined with molecular collision theory adapted to calculate frequency of contact between the susceptible population and the droplet/nuclei cloud, infection probabilities are used to define infection rate constants , ab-initio, leading to a SEIR model .
Edit intent: meaning-changed
Original:  While the initially near unity infection probability due to droplets (airborne/ballistic) rapidly decays within the first 25s, the small yet persistent infection probability of airborne desiccated nuclei decays appreciably only by  1000s  . Combined with molecular collision theory adapted to calculate frequency of contact between the susceptible population and the droplet/nuclei cloud, infection probabilities are used to define infection rate constants , ab-initio, leading to a SEIR model .
Revised:  While the initially near unity infection probability due to droplets (airborne/ballistic) rapidly decays within the first 25s, the small yet persistent infection probability of airborne desiccated nuclei decays appreciably only by 1000s ), assuming the virus sustains equally well within the dried droplet nuclei as in the droplets . Combined with molecular collision theory adapted to calculate frequency of contact between the susceptible population and the droplet/nuclei cloud, infection probabilities are used to define infection rate constants , ab-initio, leading to a SEIR model .
Edit intent: meaning-changed
Original:  While the initially near unity infection probability due to droplets (airborne/ballistic) rapidly decays within the first 25s, the small yet persistent infection probability of airborne desiccated nuclei decays appreciably only by  1000s  . Combined with molecular collision theory adapted to calculate frequency of contact between the susceptible population and the droplet/nuclei cloud, infection probabilities are used to define infection rate constants , ab-initio, leading to a SEIR model .
Revised:  While the initially near unity infection probability due to droplets (airborne/ballistic) rapidly decays within the first 25s, the small yet persistent infection probability of airborne desiccated nuclei decays appreciably only by 1000s . Combined with molecular collision theory adapted to calculate frequency of contact between the susceptible population and the droplet/nuclei cloud, infection rate constants are derived ab-initio, leading to a SEIR model .
Edit intent: clarity
Original:  While the initially near unity infection probability due to droplets (airborne/ballistic) rapidly decays within the first 25s, the small yet persistent infection probability of airborne desiccated nuclei decays appreciably only by  1000s  . Combined with molecular collision theory adapted to calculate frequency of contact between the susceptible population and the droplet/nuclei cloud, infection probabilities are used to define infection rate constants , ab-initio, leading to a SEIR model . Assuming the virus sustains equally well within the dried droplet nuclei as in the droplets, the floating nuclei leads to a stronger contribution to the corresponding rate constants with respect to the droplets, in the above-mentioned conditions. Combining both pathways, the basic reproduction number \mathcal{R Viral load, minimum infectious dose, sensitivity of the virus half-life to the phase of its vector , extent of dilution of the respiratory jet/puff by the entraining air are the important factors that determine specific physical modes of transmission and the pandemic evolution .
Revised:  While the initially near unity infection probability due to droplets (airborne/ballistic) rapidly decays within the first 25s, the small yet persistent infection probability of airborne desiccated nuclei decays appreciably only by 1000s . Combined with molecular collision theory adapted to calculate frequency of contact between the susceptible population and the droplet/nuclei cloud, infection probabilities are used to define infection rate constants , ab-initio, leading to a SEIR model applicable for any respiratory event - vector combination. Viral load, minimum infectious dose, sensitivity of the virus half-life to the phase of its vector , extent of dilution of the respiratory jet/puff by the entraining air are the important factors that determine specific physical modes of transmission and the pandemic evolution .
Edit intent: meaning-changed
Original:  Combining both pathways, the basic reproduction number \mathcal{R Viral load, minimum infectious dose, sensitivity of the virus half-life to the phase of its vector , extent of dilution of the respiratory jet/puff by the entraining air are the important factors that determine specific physical modes of transmission and the pandemic evolution .
Revised:  Combining both pathways, the basic reproduction number \mathcal{R Viral load, minimum infectious dose, sensitivity of the virus half-life to the phase of its vector and dilution of the respiratory jet/puff by the entraining air are the important factors that determine specific physical modes of transmission and the pandemic evolution .
Edit intent: clarity
Original:  Combining both pathways, the basic reproduction number \mathcal{R Viral load, minimum infectious dose, sensitivity of the virus half-life to the phase of its vector , extent of dilution of the respiratory jet/puff by the entraining air are the important factors that determine specific physical modes of transmission and the pandemic evolution .
Revised:  Combining both pathways, the basic reproduction number \mathcal{R Viral load, minimum infectious dose, sensitivity of the virus half-life to the phase of its vector , extent of dilution of the respiratory jet/puff by the entraining air are shown to mechanistically determine specific physical modes of transmission and the pandemic evolution .
Edit intent: clarity
Original:  Combining both pathways, the basic reproduction number \mathcal{R Viral load, minimum infectious dose, sensitivity of the virus half-life to the phase of its vector , extent of dilution of the respiratory jet/puff by the entraining air are the important factors that determine specific physical modes of transmission and the pandemic evolution .
Revised:  Combining both pathways, the basic reproduction number \mathcal{R Viral load, minimum infectious dose, sensitivity of the virus half-life to the phase of its vector , extent of dilution of the respiratory jet/puff by the entraining air are the important factors that determine specific physical modes of transmission and variation in the basic reproduction number \mathcal{R .
Edit intent: clarity
Original:  This model describes the cascade as a two-stage process: initially, a cascade spreads as an ordinary newsstory; a second cascade thenemerges through attempts to disclose and rectify the falsity of the news  story.
Revised:  This model describes the cascade as a two-stage process: initially, fake news spreads as a piece of ordinary news; then, when most users start recognizing the falsity of the news story.
Edit intent: meaning-changed
Original:  We show that the proposed model is superior to the current state-of-the-art methods in accurately predicting the evolution of the fake news cascades . Moreover, the proposed model can appropriately infer the correction time when some users realize the falsity of the news  .
Revised:  We show that the proposed model is superior to the current state-of-the-art methods in accurately predicting the evolution of the spread of a fake news item . Moreover, the proposed model can appropriately infer the correction time when some users realize the falsity of the news .
Edit intent: clarity
Original:  We show that the proposed model is superior to the current state-of-the-art methods in accurately predicting the evolution of the fake news cascades . Moreover, the proposed model can appropriately infer the correction time when some users realize the falsity of the news  .
Revised:  We show that the proposed model is superior to the current state-of-the-art methods in accurately predicting the evolution of the fake news cascades . Moreover, a text analysis suggests that our model appropriately infers the correction time when some users realize the falsity of the news .
Edit intent: meaning-changed
Original:  We show that the proposed model is superior to the current state-of-the-art methods in accurately predicting the evolution of the fake news cascades . Moreover, the proposed model can appropriately infer the correction time when some users realize the falsity of the news  .
Revised:  We show that the proposed model is superior to the current state-of-the-art methods in accurately predicting the evolution of the fake news cascades . Moreover, the proposed model can appropriately infer the correction time , i.e., the moment when Twitter users start realizing the falsity of the news .
Edit intent: meaning-changed
Original:  We show that the proposed model is superior to the current state-of-the-art methods in accurately predicting the evolution of the fake news cascades . Moreover, the proposed model can appropriately infer the correction time when some users realize the falsity of the news  .
Revised:  We show that the proposed model is superior to the current state-of-the-art methods in accurately predicting the evolution of the fake news cascades . Moreover, the proposed model can appropriately infer the correction time when some users realize the falsity of the news item .
Edit intent: clarity
Original: RNNs are popular dynamical models, used for processing sequential data  . Prior theoretical work in understanding the properties of RNNs has focused on models with additive interactions , where the input to a unit is a weighted sum of the output of the remaining units in network .
Revised: Recurrent neural networks (RNNs) are powerful dynamical models, used for processing sequential data . Prior theoretical work in understanding the properties of RNNs has focused on models with additive interactions , where the input to a unit is a weighted sum of the output of the remaining units in network .
Edit intent: clarity
Original: RNNs are popular dynamical models, used for processing sequential data  . Prior theoretical work in understanding the properties of RNNs has focused on models with additive interactions , where the input to a unit is a weighted sum of the output of the remaining units in network .
Revised: RNNs are popular dynamical models, widely used in machine learning (ML) for processing sequential data . Prior theoretical work in understanding the properties of RNNs has focused on models with additive interactions , where the input to a unit is a weighted sum of the output of the remaining units in network .
Edit intent: meaning-changed
Original: RNNs are popular dynamical models, used for processing sequential data  . Prior theoretical work in understanding the properties of RNNs has focused on models with additive interactions , where the input to a unit is a weighted sum of the output of the remaining units in network .
Revised: RNNs are popular dynamical models, used for processing sequential data , and also in neuroscience, to understand the emergent properties of networks of real neurons . Prior theoretical work in understanding the properties of RNNs has focused on models with additive interactions , where the input to a unit is a weighted sum of the output of the remaining units in network .
Edit intent: meaning-changed
Original: RNNs are popular dynamical models, used for processing sequential data  . Prior theoretical work in understanding the properties of RNNs has focused on models with additive interactions , where the input to a unit is a weighted sum of the output of the remaining units in network .
Revised: RNNs are popular dynamical models, used for processing sequential data . Prior theoretical work in understanding the properties of RNNs has focused on models with additive interactions .
Edit intent: clarity
Original:  However, there is ample evidence that neurons can have gating - i.e. multiplicative - interactions. Such gating interactions have significant effects on the collective dynamics of the network. Furthermore, the best performing RNNs in machine learning have gating interactions.
Revised:  However, there is ample evidence that neurons can have gating - i.e. multiplicative -- interactions, and gating is also a central feature of the best performing RNNs in machine learning have gating interactions.
Edit intent: coherence
Original:  Furthermore, the best performing RNNs in machine learning have gating interactions. Thus, gating interactions are beneficial for information processing and learning tasks. We develop a dynamical mean-field theory (DMFT) of gating to understand the dynamical regimes produced by gating .
Revised:  Furthermore, the best performing RNNs in machine learning . Here, we develop a dynamical mean-field theory (DMFT) of gating to understand the dynamical regimes produced by gating .
Edit intent: coherence