wanyu/IteraTeR_v2 huggingface dataset:
Original:  Departing from classical adaptive algorithms, the proposed method is based on a coarse grid and iteratively improves the accuracy of the solution by solving local elliptic problems identified by an a posteriori error control.
Revised:  Departing from classical adaptive algorithms, the proposed method is based on a coarse grid and iteratively improves the solution's accuracy by solving local elliptic problems identified by an a posteriori error control.
Edit intent: clarity
Original:  Based on a ] flux reconstruction strategy , a posteriori error estimators free of undetermined constants for such a scheme are derived . Numerical comparison with a classical  adaptive algorithm illustrate the efficiency and robustness of the new method.
Revised:  Based on a ] flux reconstruction strategy , a posteriori error estimators free of undetermined constants for such a scheme are derived . Numerical comparison with a classical adaptive algorithm illustrate the efficiency of the method.
Edit intent: coherence
Original: We introduce the stochastic gradient process as a continuous-time representation of the celebrated stochastic gradient descent algorithm .
Revised: We introduce the stochastic gradient process as a continuous-time representation of stochastic gradient descent algorithm .
Edit intent: clarity
Original: We introduce the stochastic gradient process as a continuous-time representation of the celebrated stochastic gradient descent algorithm .
Revised: We introduce the stochastic gradient process as a continuous-time representation of the celebrated stochastic gradient descent .
Edit intent: clarity
Original:  The dynamical system - a gradient flow - represents the gradient descent part, the process on the finite state space represents the stochastic switching among the data sets . Processes of this type are, for instance, used to model clonal populations in fluctuating environments.
Revised:  The dynamical system - a gradient flow - represents the gradient descent part, the process on the finite state space represents the random subsampling . Processes of this type are, for instance, used to model clonal populations in fluctuating environments.
Edit intent: clarity
Original:  In this case, the process converges weakly at exponential rate to any neighbourhood of the global minimum of the full target function.
Revised:  In this case, the process converges with exponential rate to any neighbourhood of the global minimum of the full target function.
Edit intent: clarity
Original:  The dynamical system - a gradient flow - represents the gradient descent part, the process on the finite state space represents the random subsampling.
Revised:  The dynamical system -- a gradient flow - represents the gradient descent part, the process on the finite state space represents the random subsampling.
Edit intent: fluency
Original:  The dynamical system - a gradient flow - represents the gradient descent part, the process on the finite state space represents the random subsampling.
Revised:  The dynamical system - a gradient flow -- represents the gradient descent part, the process on the finite state space represents the random subsampling.
Edit intent: fluency
Original:  After introducing it, we study theoretical properties of the stochastic gradient process .
Revised:  After introducing it, we study theoretical properties of the stochastic gradient process :
Edit intent: fluency
Original:  Moreover, we give assumptions under which the stochastic gradient process  is exponentially ergodic in the Wasserstein sense.
Revised:  We give conditions under which the stochastic gradient process is exponentially ergodic in the Wasserstein sense.
Edit intent: coherence
Original:  We then additionally assume that the single target functions are strongly convex and the learning rate goes to zero sufficiently slowly  .
Revised:  Then we study the case, where the learning rate goes to zero sufficiently slowly .
Edit intent: coherence
Original:  We then additionally assume that the single target functions are strongly convex and the learning rate goes to zero sufficiently slowly  .
Revised:  We then additionally assume that the single target functions are strongly convex and the learning rate goes to zero sufficiently slowly and the single target functions are strongly convex .
Edit intent: coherence
Original:  We conclude with a discussion of discretisation strategies for the stochastic gradient process and illustrate our concepts in numerical experiments.
Revised:  We conclude after a discussion of discretisation strategies for the stochastic gradient process and illustrate our concepts in numerical experiments.
Edit intent: clarity
Original:  We conclude with a discussion of discretisation strategies for the stochastic gradient process and illustrate our concepts in numerical experiments.
Revised:  We conclude with a discussion of discretisation strategies for the stochastic gradient process and numerical experiments.
Edit intent: clarity
Original: In this paper we investigate the integrality ratio of the standard LP relaxation for the metric s-t path TSP.
Revised: In this paper we investigate the integrality ratio of the standard LP relaxation for the metric s-t Path TSP.
Edit intent: fluency
Original:  We make a near-optimal choice for an auxiliary function used in the analysis of Traub and Vygen which leads to an improved upper bound for the integrality ratio of 1.5273.
Revised:  We make a near-optimal choice for an auxiliary function used in the analysis of Traub and Vygen which leads to an improved upper bound on the integrality ratio of 1.5273.
Edit intent: fluency
Original:  By taking account of the temporal operators used in the ontology and distinguishing between ontologies given in full LTL and its core, Krom and Horn fragments, we identify a hierarchy of OMQs with atomic queries by proving rewritability into either FO(<), first-order logic with the built-in linear order, or FO(<, + ), which extends FO(<) with the standard arithmetic predicate PLUS, or FO(RPR), which admits PLUS, TIMES and relational primitive recursion.
Revised:  By taking account of the temporal operators used in the ontology and distinguishing between ontologies given in full LTL and its core, Krom and Horn fragments, we identify a hierarchy of OMQs with atomic queries by proving rewritability into either FO(<), first-order logic with the built-in linear order, or FO(<, + ), which extends FO(<) with the standard arithmetic predicate PLUS, or FO(RPR), which extends FO(<) with relational primitive recursion.
Edit intent: coherence
Original:  We obtain similar hierarchies for more expressive types of queries: positive LTL-formulas, monotone MFO(<)  and arbitrary MFO(<)-formulas.
Revised:  We obtain similar hierarchies for more expressive types of queries: positive LTL-formulas, monotone MFO(<) - and arbitrary MFO(<)-formulas.
Edit intent: fluency
Original: There are striking differences in the lethality of the Covid-19 disease, from more than 90\% estimated infected persons that experience only very weak or no symptoms to cases that require ICU assistance and result in death.
Edit intent: coherence
Original:  The fatality rate escalates dramatically with age and is much larger in males than in females .
Revised:  The fatality rate escalates dramatically with age and is larger in men than women .
Edit intent: clarity
Original:  The insufficient levelof ACE2 exacerbates the inflammatory response eventually leading to death, but if the initial levels of ACE2 are high the immune system has enough time to resolve the infection before it gets to extreme consequences.
Revised:  The insufficient levelof ACE2 exacerbates the inflammatory response due to the immune system has enough time to resolve the infection before it gets to extreme consequences.
Edit intent: coherence
Original:  ACE2 is also candidate to be a prognostic factor and a risk factor for detecting population that needs stronger protection.
Revised:  ACE2 is a candidate prognostic factor for detecting population that needs stronger protection.
Edit intent: clarity
Original:  I show that these variations across age and gender are quantitatively explained by the levels of the ACE2 protein in the lungs .
Revised:  I show that these variations are strongly correlated with the levels of the ACE2 protein in the lungs .
Edit intent: clarity
Original:  Surprisingly , despite ACE2 is the viral receptor, higher values of ACE2 lead to lower fatality.
Revised:  Surprisingly , despite ACE2 is the viral receptor, higher levels lead to lower fatality.
Edit intent: clarity
Original:  This behaviour is consistent with a previous mathematical model that predicts that the speed of the virus in the organism has a maximum and then declines with  receptor level.
Revised:  This behaviour is consistent with a previous mathematical model that predicts that the speed of viral progression in the organism has a maximum and then declines with receptor level.
Edit intent: clarity
Original:  This behaviour is consistent with a previous mathematical model that predicts that the speed of the virus in the organism has a maximum and then declines with  receptor level.
Revised:  This behaviour is consistent with a previous mathematical model that predicts that the speed of the virus in the organism has a maximum and then declines with the receptor level.
Edit intent: fluency
Original:  I develop here a mathematical model based on the influence of ACE2 on the speed of viral propagation and on the negative effects of its degradation.
Revised:  I develop here a mathematical model based on the influence of ACE2 on viral propagation and on the negative effects of its degradation.
Edit intent: clarity
Original:  I show that these variations are strongly correlated with the levels of the ACE2 protein in the lungsbut surprisingly, despite ACE2 is the viral receptor, higher levels lead to lower fatality.
Revised:  I show that these variations correlate strongly with the viral receptor, higher levels lead to lower fatality.
Edit intent: clarity
Original:  This behaviour is consistent with a previous mathematical model that predicts that the speed of viral progression in the organism has a maximum and then declines with the receptor level.
Revised:  This behaviour is consistent with a previous mathematical model predicts that the speed of viral progression in the organism has a maximum and then declines with the receptor level.
Edit intent: clarity
Original:  SARS-Cov-2 degrades ACE2 and thus worsens lung injury, causes vasoconstriction, thrombotic problems, and exacerbated inflammatory response .
Revised:  SARS-Cov-2 degrades ACE2 and thus worsens lung injury, exacerbated inflammatory response .
Edit intent: coherence
Original: The COVID-19 pandemic demands the rapid identification of drug-repurpusing candidates .
Revised: The current pandemic has highlighted the need for methodologies that can quickly and reliably prioritize clinically approved compounds for their potential effectiveness for SARS-CoV-2 infections .
Edit intent: clarity
Original: A population can be immune to epidemics even if not all of its individual members are immune to the disease, just as long as sufficiently many are immune -- this is the traditional notion of herd immunity.
Revised: A population can be immune to epidemics even if not all of its individual members are immune to the disease, just as long as sufficiently many are immune - this is the traditional notion of herd immunity.
Edit intent: fluency
Original:  In the smartphone era a population can be immune to epidemics even if not a single one of its members is immune to the disease -- a notion we propose to call "digital herd immunity", which is similarly an emergent characteristic of the population.
Revised:  In the smartphone era a population can be immune to epidemics even if not a single one of its members is immune to the disease - a notion we propose to call "digital herd immunity", which is similarly an emergent characteristic of the population.
Edit intent: fluency
Original:  We believe this is a promising strategy for dealing with COVID-19 in many countries such as India, whose challenges of scale motivated us to undertake this study in the first place and whose case we discuss briefly .
Revised:  We believe this is a promising strategy for dealing with COVID-19 in many countries such as India, whose challenges of scale motivated us to undertake this study .
Edit intent: coherence
Original: A population can be immune to epidemics even if not all of its individual members are immune to the disease, just as long as sufficiently many are immune - this is the traditional notion of herd immunity.
Revised: A population can be immune to epidemics even if not all of its individual members are immune to the disease, so long as sufficiently many are immune - this is the traditional notion of herd immunity.
Edit intent: coherence
Original:  In the smartphone era a population can be immune to epidemics even if not a single one of its members is immune to the disease - a notion we propose to call "digital herd immunity", which is similarly an emergent characteristic of the population.
Revised:  In the smartphone era a population can be immune to epidemics even if not a single one of its members is immune to the disease - a notion we call "digital herd immunity", which is similarly an emergent characteristic of the population.
Edit intent: clarity
Original:  As usage decreases there is a novel " contact tracing" phase transition to an epidemic phase.
Revised:  As usage decreases there is a novel " contact-tracing phase transition" to an epidemic phase.
Edit intent: fluency
Original:  For E\subset R^2, we prove that minimizing over minimal spanning trees that connect the centers of balls of radius s, which cover E, solves the maximum distance problem.
Revised:  For E\subset R^2, we prove that minimizing over minimum spanning trees that connect the centers of balls of radius s, which cover E, solves the maximum distance problem.
Edit intent: fluency
Original: It is well-known that backward parabolic equations in which the initial condition is to be determined from a measurement at a later time instant is ill-posed.
Revised: The problem of determining the initial condition is to be determined from a measurement at a later time instant is ill-posed.
Edit intent: clarity
Original:  The theoretical error estimates are confirmed with numerical tests for one and two dimensional equations.
Revised:  The theoretical error estimates are confirmed by numerical tests for one and two dimensional equations.
Edit intent: fluency
Original:  The theoretical error estimates are confirmed with numerical tests for one and two dimensional equations.
Revised:  The theoretical error estimates are confirmed with numerical tests for one- and two-dimensional equations
Edit intent: fluency
Original:  The resolution is idempotent in a strict sense.
Revised:  This resolution is idempotent in a strict sense.
Edit intent: fluency
Original:  The resolution is idempotent in a strict sense.
Revised:  The resolution is idempotent in a strong sense.
Edit intent: clarity
Original:  The resulting nucleus displays the concept that was implicit in the original adjunction , just as the singular value decomposition of an adjoint pair of linear operators displays their canonical bases. snip In his seminal early work, Ross Street described an adjunction between monads and comonads in 2-categories.
Revised:  The nucleus of an adjunction displays its conceptual core , just as the singular value decomposition of an adjoint pair of linear operators displays their canonical bases. snip In his seminal early work, Ross Street described an adjunction between monads and comonads in 2-categories.
Edit intent: clarity
Original:  Lifting the nucleus construction, we show that the resulting Street monad on monads is strictly idempotent, and extracts the nucleus of a monad.
Revised:  Lifting the nucleus construction, we show that the resulting Street monad on monads is strongly idempotent, and extracts the nucleus of a monad.
Edit intent: clarity
Original:  This uncovers remarkably concrete applications behind a notable fragment of pure 2-category theory .
Revised:  Applying a notable fragment of pure 2-category theory .
Edit intent: clarity
Original:  These enable the aforementioned mixture of verifiability and privacy in a manner derived from public/private key pairs and digital signatures, generalised to avoid restrictive ownership of sensitive digital keys and/or data.
Revised:  These enable the aforementioned mixture of verifiability and privacy in a manner derived from public/private key pairs and digital signatures, generalized to avoid restrictive ownership of sensitive digital keys and/or data.
Edit intent: fluency
Original:  Methods: We developed a prototype mobile phone app and requisite distributed server architecture that facilitates instant verification of tamper-proof test results.
Revised:  Methods: We developed a prototype mobile phone app and requisite decentralized server architecture that facilitates instant verification of tamper-proof test results.
Edit intent: fluency
Original:  Simulations of the model, using data relevant to COVID-19 transmission in the state of New York and the entire US, show that the pandemic will peak in mid and late April, respectively.
Revised:  Simulations of the model, using data relevant to COVID-19 transmission in New York state and the entire US, show that the pandemic will peak in mid and late April, respectively.
Edit intent: clarity
Original:  These numbers decrease by 80\% and 64\%, respectively, if adherence to strict social-distancing measures is improved and maintained until the end of May or June .
Revised:  These numbers decrease by 80\% and 64\%, respectively, if the strict social-distancing measures is improved and maintained until the end of May or June .
Edit intent: clarity
Original:  These numbers decrease by 80\% and 64\%, respectively, if adherence to strict social-distancing measures is improved and maintained until the end of May or June .
Revised:  These numbers decrease by 80\% and 64\%, respectively, if adherence to strict social-distancing measures implemented are maintained until the end of May or June .
Edit intent: clarity
Original:  This study shows that early termination of strict social-distancing measures could trigger a devastating second wave with burden similar to that projected before the onset of strict social-distance measures .
Revised:  This study shows that early termination of strict social-distancing could trigger a devastating second wave with burden similar to that projected before the onset of strict social-distance measures .
Edit intent: fluency
Original:  This study shows that early termination of strict social-distancing measures could trigger a devastating second wave with burden similar to that projected before the onset of strict social-distance measures .
Revised:  This study shows that early termination of strict social-distancing measures could trigger a devastating second wave with burden similar to that projected before the onset of strict social-distance .
Edit intent: fluency
Original:  Combining low efficacy masks with improved levels of the other anti-COVID-19 intervention strategies can lead to elimination of the pandemic.
Revised:  Combining low efficacy masks with improved levels of other anti-COVID-19 intervention strategies can lead to elimination of the pandemic.
Edit intent: fluency
Original:  Combining low efficacy masks with improved levels of the other anti-COVID-19 intervention strategies can lead to elimination of the pandemic.
Revised:  Combining low efficacy masks with improved levels of the other anti-COVID-19 intervention measures can lead to elimination of the pandemic.
Edit intent: clarity
Original:  The mask coverage needed to eliminate COVID-19 decreases if the mask-use is combined with strict social-distancing.
Revised:  The mask coverage needed to eliminate COVID-19 decreases if mask-use is combined with strict social-distancing.
Edit intent: fluency
Original:  The evaluation function conveys global structure guidance for the assembling process to follow . Experimental results demonstrate that our method successfully generates combinatorial objects and simulates more realistic generation processes.
Revised:  An evaluation function conveys global structure guidance for the assembling process to follow . Experimental results demonstrate that our method successfully generates combinatorial objects and simulates more realistic generation processes.
Edit intent: fluency
Original:  Our results from model simulations imply that the receptor aggregation processes can govern the signaling activity in a regime inaccessible by previous theories.
Revised:  Our results from model simulations imply that receptor aggregation processes can govern the signaling activity in a regime inaccessible by previous theories.
Edit intent: fluency
Original:  Our results from model simulations imply that the receptor aggregation processes can govern the signaling activity in a regime inaccessible by previous theories.
Revised:  Our results from model simulations imply that the receptor aggregation processes can govern cooperative effects in a regime inaccessible by previous theories.
Edit intent: clarity
Original:  We propose algorithms that choose a point in C using only these rankings as input and we provide bounds on their distortion (worst-case approximation ratio).
Revised:  We propose algorithms that choose a point in C using only these rankings as input and we provide bounds on their distortion (worst-case approximation ratio).
Edit intent: fluency
Original:  We do so by proving a novel lemma about matching rankings of candidates to candidates, which we refer to as the ranking-matching lemma .
Revised:  We do so by proving a novel lemma about matching voters to candidates, which we refer to as the ranking-matching lemma .
Edit intent: clarity
Original:  We do so by proving a novel lemma about matching rankings of candidates to candidates, which we refer to as the ranking-matching lemma .
Revised:  We do so by proving a novel lemma about matching rankings of candidates to candidates, which we refer to as the ranking-matching lemma .
Edit intent: fluency
Original:  We also provide more refined, parameterized, bounds using the notion of \alpha -decisiveness, which quantifies the extent to which a voter may prefer her top choice relative to all others.
Revised:  We also provide more refined, parameterized, bounds using the notion of \alpha -decisiveness, which quantifies the extent to which a voter may prefer her top choice relative to all others.
Edit intent: fluency
Original:  In this paper, we introduce "entity triggers ", an effective proxy of human explanations for facilitating label-efficient learning of NER models.
Revised:  In this paper, we introduce "entity triggers ," an effective proxy of human explanations for facilitating label-efficient learning of NER models.
Edit intent: fluency
Original:  Our proposed model, named Trigger Matching Network, jointly learns trigger representations and soft matching module with self-attention such that can generalize to unseen sentences easily for tagging.
Revised:  Our proposed model, Trigger Matching Network, jointly learns trigger representations and soft matching module with self-attention such that can generalize to unseen sentences easily for tagging.
Edit intent: clarity
Original:  Experiments show that the framework is significantly more cost-effective such that using 20\% of the trigger-annotated sentences can result in a comparable performance of conventional supervised approaches using 70\% training data.
Revised:  Our framework is significantly more cost-effective such that using 20\% of the trigger-annotated sentences can result in a comparable performance of conventional supervised approaches using 70\% training data.
Edit intent: coherence