wanyu/IteraTeR_v2 huggingface dataset:
Original:  We develop its substitution, called a swapping lemma for regular languages, to prove the non-regularity of the language with advice.
Revised:  We develop its substitution, called a swapping lemma for regular languages, to prove the non-regularity of a target language with advice.
Edit intent: clarity
Original: We consider an ad hoc network which uses multihop routing and slotted ALOHA for its MAC contention .
Revised: In a wireless network the set of transmitting nodes changes frequently because of the MAC scheduler and the traffic load. Previously, connectivity in wireless networks was analyzed using static geometric graphs, and as we show leads to an overly constrained design criterion. The dynamic nature of the transmitting set introduces additional randomness in a wireless system that improves the connectivity, and this additional randomness is not captured by a static connectivity graph. In this paper, we consider an ad hoc network which uses multihop routing and slotted ALOHA for its MAC contention .
Edit intent: coherence
Original:  We derive the distributional properties of the connection time using ideas from first passage percolation and epidemic processes.
Revised:  We derive the distributional properties of the connection delay using techniques from first-passage percolation and epidemic processes.
Edit intent: clarity
Original: In this paper we have proposed a new model for visual consciousness based on the premise  there exists a quantum teleportation mechanism between the eye and the brain.
Revised: In this paper we propose a new model for visual consciousness based on the premise there exists a quantum teleportation mechanism between the eye and the brain.
Edit intent: coherence
Original: In this paper we have proposed a new model for visual consciousness based on the premise  there exists a quantum teleportation mechanism between the eye and the brain.
Revised: In this paper we have proposed a new model for visual consciousness based on the premise that there exists a quantum teleportation mechanism between the eye and the brain.
Edit intent: fluency
Original: The paper studies the problem of distributed static parameter (vector) estimation in sensor networks with nonlinear observation models and imperfect inter-sensor communication.
Revised: The paper studies distributed static parameter (vector) estimation in sensor networks with nonlinear observation models and imperfect inter-sensor communication.
Edit intent: clarity
Original: The paper studies the problem of distributed static parameter (vector) estimation in sensor networks with nonlinear observation models and imperfect inter-sensor communication.
Revised: The paper studies the problem of distributed static parameter (vector) estimation in sensor networks with nonlinear observation models and noisy inter-sensor communication.
Edit intent: clarity
Original:  We introduce the concept of separably estimable observation models , which generalize the observability condition for linear centralized estimation to nonlinear distributed estimation.
Revised:  It introduces separably estimable observation models , which generalize the observability condition for linear centralized estimation to nonlinear distributed estimation.
Edit intent: clarity
Original:  We introduce the concept of separably estimable observation models , which generalize the observability condition for linear centralized estimation to nonlinear distributed estimation.
Revised:  We introduce the concept of separably estimable observation models that generalize the observability condition for linear centralized estimation to nonlinear distributed estimation.
Edit intent: fluency
Original:  We introduce the concept of separably estimable observation models , which generalize the observability condition for linear centralized estimation to nonlinear distributed estimation.
Revised:  We introduce the concept of separably estimable observation models , which generalize the observability condition in linear centralized estimation to nonlinear distributed estimation.
Edit intent: clarity
Original:  We study the algorithms NU (with its linear counterpart LU) and \mathcal{NLU     consistency (all sensors reach consensus almost sure and converge to the true parameter value ), asymptotic unbiasedness and asymptotic normality of these algorithms.
Revised:  We study the algorithms NU (with its linear counterpart LU) and \mathcal{NLU consistency (all sensors reach consensus almost surely and converge to the true parameter value ), asymptotic unbiasedness and asymptotic normality of these algorithms.
Edit intent: fluency
Original:  While the algorithm \mathcal{NU and \mathcal{NU} are } analyzed in the framework of stochastic approximation theory , the algorithm \mathcal{NLU} exhibits mixed time-scale behavior and biased perturbations and require a different approach , which we develop in the paper.
Revised:  While the algorithm \mathcal{NU and \mathcal{NU} are } analyzed in the framework of stochastic approximation theory ; algorithm \mathcal{NLU} exhibits mixed time-scale behavior and biased perturbations and require a different approach , which we develop in the paper.
Edit intent: fluency
Original:  While the algorithm \mathcal{NU and \mathcal{NU} are } analyzed in the framework of stochastic approximation theory , the algorithm \mathcal{NLU} exhibits mixed time-scale behavior and biased perturbations and require a different approach , which we develop in the paper.
Revised:  While the algorithm \mathcal{NU and \mathcal{NU} are } analyzed in the framework of stochastic approximation theory , the algorithm \mathcal{NLU} exhibits mixed time-scale behavior and biased perturbations , and its analysis requires a different approach , which we develop in the paper.
Edit intent: coherence
Original:  While the algorithm \mathcal{NU and \mathcal{NU} are } analyzed in the framework of stochastic approximation theory , the algorithm \mathcal{NLU} exhibits mixed time-scale behavior and biased perturbations and require a different approach , which we develop in the paper.
Revised:  While the algorithm \mathcal{NU and \mathcal{NU} are } analyzed in the framework of stochastic approximation theory , the algorithm \mathcal{NLU} exhibits mixed time-scale behavior and biased perturbations and require a different approach that is developed in the paper.
Edit intent: clarity
Original: Market based instruments such as payments, auctions or tradable permits have been proposed as flexible and cost-effective instruments for biodiversity conservation on private lands.
Revised: Market-based instruments such as payments, auctions or tradable permits have been proposed as flexible and cost-effective instruments for biodiversity conservation on private lands.
Edit intent: fluency
Original:  Trading the service of conservation requires  to define a metric that determines to which extent a conserved site adds to the regional conservation objective.
Revised:  Trading the service of conservation requires one to define a metric that determines to which extent a conserved site adds to the regional conservation objective.
Edit intent: clarity
Original:  Trading the service of conservation requires  to define a metric that determines to which extent a conserved site adds to the regional conservation objective.
Revised:  Trading the service of conservation requires to define a metric that determines the extent to which a conserved site adds to the regional conservation objective.
Edit intent: fluency
Original:  In this paper, we use a coupled ecological economic simulation model to examine how spatial connectivity may be considered in metrics for conservation markets . Land use decisions, driven by changing conservation costs and the conservation market, are simulated by an agent based model of land users.
Revised:  In this paper, we use a coupled ecological economic simulation model to examine how spatial connectivity may be considered in the financial incentives created by a market-based conservation scheme . Land use decisions, driven by changing conservation costs and the conservation market, are simulated by an agent based model of land users.
Edit intent: clarity
Original:  In this paper, we use a coupled ecological economic simulation model to examine how spatial connectivity may be considered in metrics for conservation markets . Land use decisions, driven by changing conservation costs and the conservation market, are simulated by an agent based model of land users.
Revised:  In this paper, we use a coupled ecological economic simulation model to examine how spatial connectivity may be considered in metrics for conservation markets . Land use decisions, driven by changing conservation costs and the conservation market, are simulated by an agent-based model of land users.
Edit intent: fluency
Original:  We find that optimal spatial metrics correlate with species characteristics such as the dispersal distance, but they also depend on the spatio-temporal distribution of conservation costs.
Revised:  We find that optimal spatial incentives for agents correlate with species characteristics such as the dispersal distance, but they also depend on the spatio-temporal distribution of conservation costs.
Edit intent: clarity
Original:  Nevertheless, in most real money systems, the greedy algorithm can always yield optimal solutions.
Revised:  Nevertheless, in most real money systems, the greedy algorithm yields optimal solutions.
Edit intent: clarity
Original:  In this paper, we study what type of coin systems that can guarantee the optimality of the greedy algorithm.
Revised:  In this paper, we study what type of coin systems that guarantee the optimality of the greedy algorithm.
Edit intent: clarity
Original:  We provide novel proofs for the sufficient and necessary condition of the so-called canonical coin systems with four or five types of coins, and a sufficient condition of non-canonical coin systems, respectively.
Revised:  We provide new proofs for a sufficient and necessary condition of the so-called canonical coin systems with four or five types of coins, and a sufficient condition of non-canonical coin systems, respectively.
Edit intent: clarity
Original:  We provide novel proofs for the sufficient and necessary condition of the so-called canonical coin systems with four or five types of coins, and a sufficient condition of non-canonical coin systems, respectively.
Revised:  We provide novel proofs for the sufficient and necessary condition for the so-called canonical coin systems with four or five types of coins, and a sufficient condition of non-canonical coin systems, respectively.
Edit intent: fluency
Original:  We provide novel proofs for the sufficient and necessary condition of the so-called canonical coin systems with four or five types of coins, and a sufficient condition of non-canonical coin systems, respectively.
Revised:  We provide novel proofs for the sufficient and necessary condition of the so-called canonical coin systems with four or five types of coins, and a sufficient condition for non-canonical coin systems, respectively.
Edit intent: fluency
Original: In many physical  statistical, biological and other investigations it is desirable to approximate a system of points by objects of lower dimension and/or complexity.
Revised: In many physical , statistical, biological and other investigations it is desirable to approximate a system of points by objects of lower dimension and/or complexity.
Edit intent: fluency
Original:  For this purpose, Karl Pearson invented principal component analysis in 1901 and found " lines and planes of closest fit to system of points " . The famous k-means algorithm solves the approximation problem too, but by finite sets instead of lines and planes.
Revised:  For this purpose, Karl Pearson invented principal component analysis in 1901 and found ' lines and planes of closest fit to system of points " . The famous k-means algorithm solves the approximation problem too, but by finite sets instead of lines and planes.
Edit intent: fluency
Original:  For this purpose, Karl Pearson invented principal component analysis in 1901 and found " lines and planes of closest fit to system of points " . The famous k-means algorithm solves the approximation problem too, but by finite sets instead of lines and planes.
Revised:  For this purpose, Karl Pearson invented principal component analysis in 1901 and found " lines and planes of closest fit to system of points ' . The famous k-means algorithm solves the approximation problem too, but by finite sets instead of lines and planes.
Edit intent: fluency
Original:  This chapter gives a brief practical introduction into the methods of construction of general principal objects, i.e. objects embedded in the "middle" of the multidimensional data set.
Revised:  This chapter gives a brief practical introduction into the methods of construction of general principal objects, i.e. objects embedded in the 'middle' of the multidimensional data set.
Edit intent: fluency
Original:  Among the class of data fusion schemes that enable optimal inference at the fusion center for Markov random field  hypotheses, the minimum per-sensor energy cost is bounded below by a minimum spanning tree data fusion and above by a suboptimal scheme  referred to as Data Fusion for Markov Random Field (DFMRF).
Revised:  Among the class of data fusion schemes that enable optimal inference at the fusion center for Markov random field (MRF) hypotheses, the minimum per-sensor energy cost is bounded below by a minimum spanning tree data fusion and above by a suboptimal scheme referred to as Data Fusion for Markov Random Field (DFMRF).
Edit intent: clarity
Original:  Among the class of data fusion schemes that enable optimal inference at the fusion center for Markov random field  hypotheses, the minimum per-sensor energy cost is bounded below by a minimum spanning tree data fusion and above by a suboptimal scheme  referred to as Data Fusion for Markov Random Field (DFMRF).
Revised:  Among the class of data fusion schemes that enable optimal inference at the fusion center for Markov random field hypotheses, the scheme with minimum average energy consumption is bounded below by a minimum spanning tree data fusion and above by a suboptimal scheme referred to as Data Fusion for Markov Random Field (DFMRF).
Edit intent: clarity
Original:  Among the class of data fusion schemes that enable optimal inference at the fusion center for Markov random field  hypotheses, the minimum per-sensor energy cost is bounded below by a minimum spanning tree data fusion and above by a suboptimal scheme  referred to as Data Fusion for Markov Random Field (DFMRF).
Revised:  Among the class of data fusion schemes that enable optimal inference at the fusion center for Markov random field hypotheses, the minimum per-sensor energy cost is bounded below by a minimum spanning tree , and above by a suboptimal scheme referred to as Data Fusion for Markov Random Field (DFMRF).
Edit intent: clarity
Original:  Among the class of data fusion schemes that enable optimal inference at the fusion center for Markov random field  hypotheses, the minimum per-sensor energy cost is bounded below by a minimum spanning tree data fusion and above by a suboptimal scheme  referred to as Data Fusion for Markov Random Field (DFMRF).
Revised:  Among the class of data fusion schemes that enable optimal inference at the fusion center for Markov random field hypotheses, the minimum per-sensor energy cost is bounded below by a minimum spanning tree data fusion and above by a suboptimal scheme , referred to as Data Fusion for Markov Random Field (DFMRF).
Edit intent: fluency
Original:  Among the class of data fusion schemes that enable optimal inference at the fusion center for Markov random field  hypotheses, the minimum per-sensor energy cost is bounded below by a minimum spanning tree data fusion and above by a suboptimal scheme  referred to as Data Fusion for Markov Random Field (DFMRF).
Revised:  Among the class of data fusion schemes that enable optimal inference at the fusion center for Markov random field hypotheses, the minimum per-sensor energy cost is bounded below by a minimum spanning tree data fusion and above by a suboptimal scheme referred to as Data Fusion for Markov Random Fields (DFMRF).
Edit intent: fluency
Original:  While ordinary differential equation (ODE) models remain the conceptual framework for modelling many cellular processes, specific situations demand stochastic models to capture the influence of noise.
Revised:  While ordinary differential equations (ODEs) form the conceptual framework for modelling many cellular processes, specific situations demand stochastic models to capture the influence of noise.
Edit intent: clarity
Original:  While stochastic simulations are a practical way to realise the CME, analytical approximations offer more insights into the influence of noise on cell function.
Revised:  While stochastic simulations are a practical way to realise the CME, analytical approximations offer more insight into the influence of noise on cell function.
Edit intent: fluency
Original:  Towards this end, the recently developed two-moment approximation (2MA) is a promising approach, accounting for the coupling between the means and ( co)variances.
Revised:  Towards this end, the two-moment approximation (2MA) is a promising approach, accounting for the coupling between the means and ( co)variances.
Edit intent: clarity
Original:  We extend the derivation of the 2MA by establishing two advances to previous efforts: a) relative concentrations and b) non-elementary reactions.
Revised:  We extend previous derivations of 2MA by establishing two advances to previous efforts: a) relative concentrations and b) non-elementary reactions.
Edit intent: fluency
Original:  We extend the derivation of the 2MA by establishing two advances to previous efforts: a) relative concentrations and b) non-elementary reactions.
Revised:  We extend the derivation of the 2MA by allowing a) non-elementary reactions and b) non-elementary reactions.
Edit intent: clarity
Original:  We demonstrate this 2MA approach with an application to the well established fission yeast cell cycle model.
Revised:  We demonstrate this 2MA approach to the well established fission yeast cell cycle model.
Edit intent: clarity
Original:  It was previously proposed that the late Ordovician extinction is a  candidate for a contribution from an ionizing radiation event, based on environmental selectivity in trilobites.
Revised:  It was previously proposed that the late Ordovician extinction is a plausible candidate for a contribution from an ionizing radiation event, based on environmental selectivity in trilobites.
Edit intent: clarity
Original:  However, the patterns are not sufficiently selective as to be said to provide strong evidence for the ionizing radiation hypothesis.
Edit intent: coherence
Original: Based on the intensity and rates of various kinds of intense ionizing radiation events such as supernovae and gamma-ray bursts, it is likely that the Earth has been subjected to one or more events of potential mass extinction level intensity during the Phanerozoic.
Revised: Based on the intensity and rates of various kinds of intense ionizing radiation events such as supernovae and gamma-ray bursts, it is likely that the Earth has been subjected to one or extinction level events during the Phanerozoic.
Edit intent: clarity
Original:  These induce changes in atmospheric chemistry so that the level of Solar ultraviolet-B radiation reaching  surface and near-surface waters may be approximately doubled for up to one decade.
Revised:  These induce changes in atmospheric chemistry so that the level of Solar ultraviolet-B radiation reaching the surface and near-surface waters may be approximately doubled for up to one decade.
Edit intent: fluency
Original:  These induce changes in atmospheric chemistry so that the level of Solar ultraviolet-B radiation reaching  surface and near-surface waters may be approximately doubled for up to one decade.
Revised:  These induce changes in atmospheric chemistry so that the level of Solar ultraviolet-B radiation reaching surface and near-surface waters may be doubled for up to one decade.
Edit intent: clarity
Original:  These induce changes in atmospheric chemistry so that the level of Solar ultraviolet-B radiation reaching  surface and near-surface waters may be approximately doubled for up to one decade.
Revised:  These induce changes in atmospheric chemistry so that the level of Solar ultraviolet-B radiation reaching surface and near-surface waters may be approximately doubled for up to a decade.
Edit intent: clarity
Original:  Certain regularities in the latitudinal distribution of damage are apparent in computational simulations of the atmospheric changes.
Revised:  Regularities in the latitudinal distribution of damage are apparent in computational simulations of the atmospheric changes.
Edit intent: clarity
Original:  Certain regularities in the latitudinal distribution of damage are apparent in computational simulations of the atmospheric changes.
Revised:  Certain regularities in the latitudinal distribution of damage are apparent in simulations of the atmospheric changes.
Edit intent: clarity
Original:  It was previously proposed that the late Ordovician extinction is a plausible candidate for a contribution from an ionizing radiation event, based on environmental selectivity in trilobites.
Revised:  We previously proposed that the late Ordovician extinction is a plausible candidate for a contribution from an ionizing radiation event, based on environmental selectivity in trilobites.
Edit intent: coherence
Original:  In order to test a null hypothesis based on this proposal, we confront latitudinal differential extinction rates predicted from the simulations with data from a published analysis of latitudinal gradients in the Ordovician extinction.
Revised:  To test a null hypothesis based on this proposal, we confront latitudinal differential extinction rates predicted from the simulations with data from a published analysis of latitudinal gradients in the Ordovician extinction.
Edit intent: coherence
Original:  We predict that any land mass (such as part of north China  ) which then lay about 20 degrees or more north of the equator should be a refugium from the UVB effects, and show a different pattern of extinction in the first strike of the end-Ordovician extinction, if it were induced by such a radiation event.
Revised:  We predict that any land mass (such as parts of north China ) which then lay about 20 degrees or more north of the equator should be a refugium from the UVB effects, and show a different pattern of extinction in the first strike of the end-Ordovician extinction, if it were induced by such a radiation event.
Edit intent: fluency
Original:  We predict that any land mass (such as part of north China  ) which then lay about 20 degrees or more north of the equator should be a refugium from the UVB effects, and show a different pattern of extinction in the first strike of the end-Ordovician extinction, if it were induced by such a radiation event.
Revised:  We predict that any land mass (such as part of north China ) which then lay north of the equator should be a refugium from the UVB effects, and show a different pattern of extinction in the first strike of the end-Ordovician extinction, if it were induced by such a radiation event.
Edit intent: clarity
Original:  We predict that any land mass (such as part of north China  ) which then lay about 20 degrees or more north of the equator should be a refugium from the UVB effects, and show a different pattern of extinction in the first strike of the end-Ordovician extinction, if it were induced by such a radiation event.
Revised:  We predict that any land mass (such as part of north China ) which then lay about 20 degrees or more north of the equator should be a refuge from UVB effects, and show a different pattern of extinction in the first strike of the end-Ordovician extinction, if it were induced by such a radiation event.
Edit intent: fluency