wanyu/IteraTeR_full_sent huggingface dataset:
Original:  In this paper, we present the first examples of n-vertex trees for n\in\{13,14,16,17,18,19,20\} that require strictly more points than vertices to admit an L-shaped embedding , proving that f_4(n)\geq n+1 for those n . Moreover, using computer assistance , we show that every tree on n\leq 11 vertices admits an L-shaped embedding in every set of n points , proving that f_d(n) = n, d\in\{3, 4\ .
Revised:  In this paper, we present the first examples of n-vertex trees for n\in\{13,14,16,17,18,19,20\} that require strictly more points than vertices to admit an L-shaped embedding , proving that f_4(n)\geq n+1 for those n . Moreover, using computer help , we show that every tree on n\leq 11 vertices admits an L-shaped embedding in every set of n points , proving that f_d(n) = n, d\in\{3, 4\ .
Edit intent: fluency
Original:  In this paper, we present the first examples of n-vertex trees for n\in\{13,14,16,17,18,19,20\} that require strictly more points than vertices to admit an L-shaped embedding , proving that f_4(n)\geq n+1 for those n . Moreover, using computer assistance , we show that every tree on n\leq 11 vertices admits an L-shaped embedding in every set of n points , proving that f_d(n) = n, d\in\{3, 4\ .
Revised:  In this paper, we present the first examples of n-vertex trees for n\in\{13,14,16,17,18,19,20\} that require strictly more points than vertices to admit an L-shaped embedding , proving that f_4(n)\geq n+1 for those n . Moreover, using computer assistance , we show that every tree on n\leq 12 vertices admits an L-shaped embedding in every set of n points , proving that f_d(n) = n, d\in\{3, 4\ .
Edit intent: meaning-changed
Original:  In this paper, we present the first examples of n-vertex trees for n\in\{13,14,16,17,18,19,20\} that require strictly more points than vertices to admit an L-shaped embedding , proving that f_4(n)\geq n+1 for those n . Moreover, using computer assistance , we show that every tree on n\leq 11 vertices admits an L-shaped embedding in every set of n points , proving that f_d(n) = n, d\in\{3, 4\ .
Revised:  In this paper, we present the first examples of n-vertex trees for n\in\{13,14,16,17,18,19,20\} that require strictly more points than vertices to admit an L-shaped embedding , proving that f_4(n)\geq n+1 for those n . Moreover, using computer assistance , we show that every tree on n\leq 11 vertices admits an L-shaped embedding in every set of n points . We also consider embedding ordered trees, where the cyclic order of the neighbors of each vertex in the embedding is prescribed. For this setting, we determine the smallest non-embeddable ordered tree on n = n, d\in\{3, 4\ .
Edit intent: meaning-changed
Original:  In this paper, we present the first examples of n-vertex trees for n\in\{13,14,16,17,18,19,20\} that require strictly more points than vertices to admit an L-shaped embedding , proving that f_4(n)\geq n+1 for those n . Moreover, using computer assistance , we show that every tree on n\leq 11 vertices admits an L-shaped embedding in every set of n points , proving that f_d(n) = n, d\in\{3, 4\ .
Revised:  In this paper, we present the first examples of n-vertex trees for n\in\{13,14,16,17,18,19,20\} that require strictly more points than vertices to admit an L-shaped embedding , proving that f_4(n)\geq n+1 for those n . Moreover, using computer assistance , we show that every tree on n\leq 11 vertices admits an L-shaped embedding in every set of n points , proving that f_d(n) = 10 vertices, and we show that every ordered tree on n\leq 9 or n=11 vertices admits an L-shaped embedding in every set of n points. We also construct an infinite family of ordered trees which do not always admit an L-shaped embedding, answering a question raised by Biedl, Chan, Derka, Jain, and Lubiw .
Edit intent: meaning-changed
Original:  There has been considerable work on establishing upper bounds on the minimum cardinality such that any point set of that size admits an L-shaped embedding of any n-vertex tree with maximum degree 4.
Revised:  There has been considerable work on establishing upper bounds on the minimum cardinality such that any point set of that size admits an L-shaped embedding of any n-vertex tree with maximum degree 4 admits an L-shaped embedding on the point set.
Edit intent: clarity
Original: In 2012, URLan accumulated a USD  6.2 billion loss on a credit derivatives portfolio, the so-called "London Whale" , partly as a consequence of de-correlations of non-perfectly correlated positions that were supposed to hedge each other.
Revised: In 2012, URLan accumulated a USD ~ 6.2 billion loss on a credit derivatives portfolio, the so-called "London Whale" , partly as a consequence of de-correlations of non-perfectly correlated positions that were supposed to hedge each other.
Edit intent: clarity
Original: In 2012, URLan accumulated a USD  6.2 billion loss on a credit derivatives portfolio, the so-called "London Whale" , partly as a consequence of de-correlations of non-perfectly correlated positions that were supposed to hedge each other.
Revised: In 2012, URLan accumulated a USD 6.2 billion loss on a credit derivatives portfolio, the so-called `London Whale' , partly as a consequence of de-correlations of non-perfectly correlated positions that were supposed to hedge each other.
Edit intent: fluency
Original:  Since our findings are particularly relevant for large portfolios, where even small correlation changes can have a large impact, a further application would be to stress-test portfolios of central counterparties, which are of systemically relevant size.
Revised:  Since our findings are particularly relevant for large portfolios, where even small correlation changes can have a large impact, a further application would be to stress test portfolios of central counterparties, which are of systemically relevant size.
Edit intent: fluency
Original:  We prove a central limit theorem and propose a computationally efficient construction for confidence intervals  .
Revised:  We prove a central limit theorem and propose a computationally efficient construction for confidence intervals . Moving to a causal inference application, we discuss the merits of local regression adjustments for heterogeneous treatment effect estimation, and give an example on a dataset exploring the effect word choice has on attitudes to the social safety net. Last, we include simulation results on real and generated data .
Edit intent: meaning-changed
Original: Computerized models of the cerebral vasculature are becoming increasingly used for analysis of medical images, patient treatment planning and cerebral haemodynamics simulations. Previously, we presented a method based on universal physical and physiological principles for the growth of realistic arterial trees in-silico using simulated annealing (SA). SA was found to be capable of reliably identifying the optimal arrangement of arteries to supply the heart.
Revised: The cerebral arteries are difficult to reproduce from first principles, featuring interwoven territories, and intricate layers of grey and white matter with differing metabolic demand. The aim of this study was to supply the heart.
Edit intent: meaning-changed
Original:  SA was found to be capable of reliably identifying the optimal arrangement of arteries to supply the heart. In this paper, we extract volumes representing the gray and white matter of the brain from Magnetic Resonance Imaging (MRI) data and automatically generate the optimal arterial tree using simulated annealing .
Revised:  SA was found to be capable of reliably identifying the optimal arrangement of arteries to identify the ideal configuration of arteries required to sustain an entire brain hemisphere based on minimisation of the energy required to supply the tissue. The 3D distribution of grey and white matter of the brain from Magnetic Resonance Imaging (MRI) data and automatically generate the optimal arterial tree using simulated annealing .
Edit intent: meaning-changed
Original:  In this paper, we extract volumes representing the gray and white matter of the brain from Magnetic Resonance Imaging (MRI) data and automatically generate the optimal arterial tree using simulated annealing .
Revised:  In this paper, we extract volumes representing the gray and white matter within a healthy human brain was first segmented from Magnetic Resonance Imaging (MRI) data and automatically generate the optimal arterial tree using simulated annealing .
Edit intent: meaning-changed
Original:  In this paper, we extract volumes representing the gray and white matter of the brain from Magnetic Resonance Imaging (MRI) data and automatically generate the optimal arterial tree using simulated annealing . The cerebral arteriesare arguably the most difficult to reproduce from first principles, featuring multiple substrates and interwoven territories , with a complicated layered topology. Comparison of our simulations with human angiography data confirms that vascular trees generated by our algorithm are a good match to real cerebral arteries .
Revised:  In this paper, we extract volumes representing the gray and white matter of the brain from Magnetic Resonance Images. A novel simulated annealing algorithm was then applied to determine the optimal configuration of arteries required to supply brain tissue. The model is validated through comparison of this ideal, entirely optimised, brain vasculature with the known structure of real arteries. This establishes that the human cerebral vasculature is highly optimised; closely resembling the most energy efficient arrangement of vessels. In addition to local adherence to fluid dynamics optimisation principles, the optimised vasculature reproduces global brain perfusion territories with well defined boundaries between anterior, middle and posterior regions. This validated brain vascular model and algorithm can be used for patient-specific modelling of stroke and cerebral haemodynamics, identification of sub-optimal conditions associated with vascular disease, and optimising vascular structures for tissue engineering and URLan design .
Edit intent: meaning-changed
Original:  Using a systems approach established in Mendelian randomization and Bayesian Network, we integrated genetic and transcriptomic data from  common-mind consortium and identified transcriptomic causal networks in observational studies.
Revised:  Using a systems approach established in Mendelian randomization and Bayesian Network, we integrated genetic and transcriptomic data from the common-mind consortium and identified transcriptomic causal networks in observational studies.
Edit intent: fluency
Original: An econometric or statistical model may undergo a marginal gain when a new variable is admitted , and a marginal loss if  an existing variable is removed. The value of a variable to the model is quantified by its expected marginal gain and marginal loss .
Revised: An econometric or statistical model may undergo a marginal gain when a new variable is admitted , and a marginal loss if an existing variable from the model. We quantify the value of a variable to the model is quantified by its expected marginal gain and marginal loss .
Edit intent: clarity
Original:  Simulation studies show that our new approaches significantly outperform a few practice-used variable selection methods  .
Revised:  Simulation studies show that our new approaches significantly outperform a few practice-used variable selection methods used in practice. The tools employed are concepts from cooperative game theory, and the results explore several novel features of the Shapley value. We even bridge the Shapley value and the Banzhaf value with binomial distributions .
Edit intent: meaning-changed
Original:  If the volatility process admits a Volterra type representation, then the model is called a Volterra typeGaussian stochastic volatility model. The scaling regimes associated with a Gaussian stochastic volatility model are split into three groups: the large deviation group, the moderate deviation group, and the central limit group .
Revised:  If the volatility process admits a Volterra type representation, then the model is of Volterra type. Three scaling regimes associated with a Gaussian stochastic volatility model are split into three groups: the large deviation group, the moderate deviation group, and the central limit group .
Edit intent: clarity
Original:  We prove a sample path large deviation principle for the log-price process in a Volterra type Gaussian stochastic volatility model , and a sample path moderate deviation principle for the same process in a Gaussian stochastic volatility model.
Revised:  We prove a sample path large deviation principle for the log-price process in a Volterra type Gaussian stochastic volatility model and a sample path moderate deviation principle for the same process in a Gaussian stochastic volatility model.
Edit intent: fluency
Original:  Another problem addressed in the paper concerns exponential moment explosions for the driftless log-price and moment explosions for the asset price in Gaussian stochastic volatility models .
Revised:  Another problem addressed in the paper concerns exponential moment explosions for the driftless log-price and moment explosions for the asset price in Gaussian stochastic volatility model with the volatility function growing faster than linearly, all the moments of order greater than one are infinite. Moment explosions are also characterized in the case of negatively correlated models, and partial results are obtained for positively correlated ones .
Edit intent: meaning-changed
Original:  Moment explosions are also characterized in the case of negatively, where \rho is the correlation coefficient, are shown for } correlated models, and partial results are obtained for positively correlated ones .
Revised:  Explosions of all the moments of order \gamma>(1-\rho^2)^{-1, where \rho is the correlation coefficient, are shown for } correlated models, and partial results are obtained for positively correlated ones .
Edit intent: meaning-changed
Original:  Moment explosions are also characterized in the case of negatively, where \rho is the correlation coefficient, are shown for } correlated models, and partial results are obtained for positively correlated ones .
Revised:  Moment explosions are also characterized in the case of negatively, where \rho is the correlation coefficient, are shown for } correlated models, and partial results are obtained for the case where \gamma=(1-\rho^2)^{-1 .
Edit intent: meaning-changed
Original: In this paper, we study Gaussian stochastic volatility models. The evolution of volatility in such a model is described by a stochastic process, which can be represented as a nonnegative continuous function of a continuous Gaussian process. If the volatility process exhibits fractional features, then the model is called a Gaussian fractional stochastic volatility model. Important examples of fractional volatility processes are fractional Brownian motion, the Riemann-Liouville fractional Brownian motion, and the fractional Ornstein-Uhlenbeck process. If the volatility process admits a Volterra type representation, then the model is of Volterra type. In the paper, we provide a unified approach to various scaling regimes associated with Gaussian models. More precisely, large deviation, moderate deviation, and central limit scalings are introduced in the paper. We prove a sample path large deviation principle for the log-price process in a Volterra type Gaussian stochastic volatility model and a sample path moderate deviation principle for the same process in a Gaussian stochastic volatility model.
Revised: In this paper, we establish sample path large deviation principle for the log-price process in a Volterra type Gaussian stochastic volatility model and a sample path moderate deviation principle for the same process in a Gaussian stochastic volatility model.
Edit intent: coherence
Original:  We prove a sample path large deviation principle for the log-price process in a Volterra type Gaussian stochastic volatility model and a sample path moderate deviation principle for the same process in a Gaussian stochastic volatility model.
Revised:  We prove a sample path large and moderate deviation principles for log-price process in a Volterra type Gaussian stochastic volatility model and a sample path moderate deviation principle for the same process in a Gaussian stochastic volatility model.
Edit intent: clarity
Original:  We prove a sample path large deviation principle for the log-price process in a Volterra type Gaussian stochastic volatility model and a sample path moderate deviation principle for the same process in a Gaussian stochastic volatility model. We also study the asymptotic behavior of  call pricing functions  and the implied volatility in mixed scaling regimes.
Revised:  We prove a sample path large deviation principle for the log-price process in a Volterra type Gaussian stochastic volatility model and a sample path moderate deviation principle for the same process in a Gaussian stochastic volatility models, and study the asymptotic behavior of call pricing functions and the implied volatility in mixed scaling regimes.
Edit intent: coherence
Original:  We also study the asymptotic behavior of  call pricing functions  and the implied volatility in mixed scaling regimes. It is also shown that tail estimates arising in the large deviation theory are locally uniform. Another problem addressed in the paper concerns moment explosions for the asset price process in a Gaussian stochastic volatility model. We prove that for the asset price process in an uncorrelated Gaussian stochastic volatility model with the volatility function growing faster than linearly,  all the moments of order greater than one are infinite.
Revised:  We also study the asymptotic behavior of call pricing functions and the implied volatility . In addition, we prove that if the volatility function in an uncorrelated Gaussian stochastic volatility model with the volatility function growing faster than linearly, all the moments of order greater than one are infinite.
Edit intent: clarity
Original:  We prove that for the asset price process in an uncorrelated Gaussian stochastic volatility model with the volatility function growing faster than linearly,  all the moments of order greater than one are infinite.
Revised:  We prove that for the asset price process in an uncorrelated Gaussian stochastic volatility model with the volatility function growing faster than linearly, then, for the asset price process, all the moments of order greater than one are infinite.
Edit intent: meaning-changed
Original:  Explosions of all the moments of order \gamma>(1-\rho^2)^{-1, where \rho is the correlation coefficient, are shown for correlated models, and partial }  results are obtained for the case where \gamma=(1-\rho^2)^{-1 .
Revised:  , where \rho is the correlation coefficient, are shown for correlated models, and partial } results are obtained for the case where \gamma=(1-\rho^2)^{-1 .
Edit intent: coherence
Original:  Explosions of all the moments of order \gamma>(1-\rho^2)^{-1, where \rho is the correlation coefficient, are shown for correlated models, and partial }  results are obtained for the case where \gamma=(1-\rho^2)^{-1 .
Revised:  Explosions of all the moments of order \gamma>(1-\rho^2)^{-1, where \rho is the correlation coefficient, are shown for correlated models, and partial } Similar moment explosion results are obtained for the case where \gamma=(1-\rho^2)^{-1 .
Edit intent: meaning-changed
Original:  Explosions of all the moments of order \gamma>(1-\rho^2)^{-1, where \rho is the correlation coefficient, are shown for correlated models, and partial }  results are obtained for the case where \gamma=(1-\rho^2)^{-1 .
Revised:  Explosions of all the moments of order \gamma>(1-\rho^2)^{-1, where \rho is the correlation coefficient, are shown for correlated models, and partial } results are obtained for correlated models .
Edit intent: clarity
Original: We consider two types of problems associated with a bufferless server with service preemption (push-out). One type is motivated by "adversarial" coupon collection with applications to modeling the surveillance of a set of servers by a botnet planning a DDoS attack on them collectively. The servers dynamically change according to a moving-target defense. Another type of problem has to do with a sequence of messages handled by the (transmission) server wherein each message obsoletes all previous ones .
Revised: A queueing system handling a sequence of message arrivals is considered where each message obsoletes all previous ones .
Edit intent: clarity
Original:  The objective is to assess the freshness of the latest message/information that has been successfully transmitted, i.e., "age of information"  .
Revised:  The objective is to assess the freshness of the latest message/information that has been successfully transmitted, i.e., "age of information" (AoI). We study a variation of traditional AoI, the "Relative AoI", here defined so as to account for the presence of newly arrived messages/information to the queue to be transmitted. Both unbuffered and buffered systems are considered .
Edit intent: meaning-changed
Original: In 2000, Elowitz and Leibler introduced the repressilator -- a synthetic gene circuit with three genes that cyclically repress transcription of the next -- as well as a corresponding mathematical model.
Revised: In 2000, Elowitz and Leibler introduced the repressilator -- a synthetic gene circuit with three genes that cyclically repress transcription of the next gene--as well as a corresponding mathematical model.
Edit intent: fluency
Original:  Finally, we derive new rates functions describing transcription rates which arise under more reasonable biological assumptions than the widely used single-step binding assumptions.
Revised:  Finally, we derive new rates functions describing transcription rates which arise under more reasonable biological assumptions than the widely used single-step binding assumption. With this new transcription-rate function, we compare the model's amplitude and period with that of a model with the conventional transcription-rate function.
Edit intent: meaning-changed
Original:  We find a family of neural network models in which memory is acquired by means of biologically-inspired learning rules; the properties of these rules, in turn, determine the storing component in which memory can persist indefinitely. Memory representations manifest as time-varying attractors in neural state-space and support associative retrieval of learned information.
Revised:  We find a simple and general principle, stemming from stability arguments, that links eigenvalues in the complex plane to memories. Specifically, imaginary-coded memories are more resilient to noise and homeostatic plasticity than their real-coded counterparts. Memory representations are stored as time-varying attractors in neural state-space and support associative retrieval of learned information.
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Original: We show that a law-invariant pricing functional defined on a general Orlicz space is typically incompatible with frictionless risky assets in the sense that one and only one of the following alternatives can hold: Either every risky payoff has a strictly-positive bid-ask spread or the pricing functional is given by an expectation and, hence, every payoff has zero bid-ask spread.
Revised: We establish general versions of a variety of results for quasiconvex, lower-semicontinuous, and law-invariant pricing functional defined on a general Orlicz space is typically incompatible with frictionless risky assets in the sense that one and only one of the following alternatives can hold: Either every risky payoff has a strictly-positive bid-ask spread or the pricing functional is given by an expectation and, hence, every payoff has zero bid-ask spread.
Edit intent: meaning-changed