wanyu/IteraTeR_v2 huggingface dataset:
Original: We prove the conjecture of Albertson stating that every planar graph can be 5-list-colored even if it contains precolored vertices, as long as they are sufficiently far apart from each other.
Revised: We answer positively the question of Albertson asking whether every planar graph can be 5-list-colored even if it contains precolored vertices, as long as they are sufficiently far apart from each other.
Edit intent: clarity
Original: We investigate the pattern formation of colony generated by chemotactic bacteria through a continuum model .
Revised: Colonies of bacteria grown on thin agar plate exhibit fractal patterns as a result of adaptation to their environments. The bacterial colony pattern formation is regulated crucially by chemotaxis, the movement of cells along a chemical concentration gradient. Here, the dynamics of pattern formation in bacterial colony is investigated theoretically through a continuum model .
Edit intent: coherence
Original:  Starting from a reduced three-compartment model of a single pyramidal neuron, we derive an observation model for dendritic dipole currents in extracellular space and thereby for the dendritic field potential that contributes to the local field potential of a neural population.
Revised:  Starting from a reduced threecompartment model of a single pyramidal neuron, we derive an observation model for dendritic dipole currents in extracellular space and thereby for the dendritic field potential that contributes to the local field potential of a neural population.
Edit intent: fluency
Original:  As a theoretical challenge, the study of  detailed-balance  violating decision rules is needed to decide whether conclusions based on models obeying detailed-balance  are indeed robust and generic.
Revised:  As a theoretical challenge, the study of so-called " detailed-balance violating decision rules is needed to decide whether conclusions based on models obeying detailed-balance are indeed robust and generic.
Edit intent: clarity
Original:  As a theoretical challenge, the study of  detailed-balance  violating decision rules is needed to decide whether conclusions based on models obeying detailed-balance  are indeed robust and generic.
Revised:  As a theoretical challenge, the study of detailed-balance " violating decision rules is needed to decide whether conclusions based on models obeying detailed-balance are indeed robust and generic.
Edit intent: fluency
Original:  As a theoretical challenge, the study of  detailed-balance  violating decision rules is needed to decide whether conclusions based on models obeying detailed-balance  are indeed robust and generic.
Revised:  As a theoretical challenge, the study of detailed-balance violating decision rules is needed to decide whether conclusions based on models obeying detailed-balance ) are indeed robust and generic.
Edit intent: fluency
Original: The typical view in evolutionary biology is that mutation rates are minimised.
Revised: A common view in evolutionary biology is that mutation rates are minimised.
Edit intent: clarity
Original:  Contrary to that view , studies in combinatorial optimisation and search have shown a clear advantage of using variable mutation rates as a control parameter to optimise the performance of evolutionary algorithms.
Revised:  However , studies in combinatorial optimisation and search have shown a clear advantage of using variable mutation rates as a control parameter to optimise the performance of evolutionary algorithms.
Edit intent: clarity
Original:  Ronald Fisher's work is the basis of much biological theory in this area .
Revised:  Much biological theory in this area .
Edit intent: clarity
Original:  He used Euclidean geometry of continuous, infinite phenotypic spaces to study the relation between mutation size and expected fitness of the offspring  .
Revised:  He used Euclidean geometry to study the relation between mutation size and expected fitness of the offspring .
Edit intent: clarity
Original:  He used Euclidean geometry of continuous, infinite phenotypic spaces to study the relation between mutation size and expected fitness of the offspring  .
Revised:  He used Euclidean geometry of continuous, infinite phenotypic spaces to study the relation between mutation size and expected fitness of the offspring in infinite phenotypic spaces .
Edit intent: clarity
Original:  Here we develop a general theory of optimal mutation rate control that is based on the alternative geometry of discrete and finite spaces of DNA sequences.
Revised:  Here we reconsider this theory based on the alternative geometry of discrete and finite spaces of DNA sequences.
Edit intent: clarity
Original:  We define the monotonic properties of fitness landscapes, which allows us to relate fitness to the topology of genotypes and mutation size.
Edit intent: coherence
Original:  First, we consider the case of a perfectly monotonic fitness landscape, in which the optimal mutation rate control functions can be derived exactly or approximately depending on additional constraints of the problem.
Revised:  First, we consider the case of a perfectly monotonic fitness landscape, in which the optimal mutation rate control can be solved exactly or approximately depending on additional constraints of the problem.
Edit intent: clarity
Original:   We discuss the relevance of these findings to living organisms , including the phenomenon of stress-induced mutagenesis .
Revised:  We discuss the relevance of these findings to living organisms .
Edit intent: clarity
Original:  We propose History-Register Automata (HRA), a new automata-theoretic formalism for modelling and verifying such programs.
Revised:  We propose History-Register Automata (HRA), a new automata-theoretic formalism for modelling such programs.
Edit intent: clarity
Original:  We show that the combination of consumption and reset capabilities renders the automata powerful enough to imitate counter machines , and in particular reset Petri nets , and yields closure under all regular operations apart from complementation.
Revised:  We show that the combination of consumption and reset capabilities renders the automata powerful enough to imitate counter machines , and yields closure under all regular operations apart from complementation.
Edit intent: coherence
Original:  Drawing on previous work where a global database of energy resource economic potential was constructed, this work uses cost distributions of non-renewable resources in order to evaluate global flows of energy commodities.
Revised:  Drawing on previous work where a global database of energy resource economic potentials was constructed, this work uses cost distributions of non-renewable resources in order to evaluate global flows of energy commodities.
Edit intent: fluency
Original:   The theory is however designed for use within economic models and models of technological change such as the Future Technology Transformations (FTT) family of models .
Revised:  The theory is however designed for use within economic or technology models that allow technology substitutions .
Edit intent: clarity
Original:  In this work, it is implemented in the global power sector model FTT:Power , with which scenarios of global resource use and marginal costs of production of energy commodities are detailed . Policy implications are given.
Revised:  In this work, it is implemented in the global power sector model FTT:Power . Policy implications are given.
Edit intent: coherence
Original:  Hence, assessing the influence of spatial proximity between scientists is crucial to promote efficient collaboration strategies and, ultimately, to improve the quality of science.
Edit intent: coherence
Original:  Here we present a systematic analysis of citation and collaboration streams between cities and countries .
Revised:  Here we present a systematic analysis of citation and collaboration networks between cities and countries .
Edit intent: clarity
Original:  By assigning papers to the geographic locations of their authors' affiliations , we construct weighted networks of citations and collaborations .
Revised:  By assigning papers to the geographic locations of their authors' affiliations .
Edit intent: clarity
Original:  However, the average impact reveals a peculiar threshold effect: the scientific output of a country may reach an impact larger than the world average only if the country invests more than 120 ,000 US per researcher annually .
Revised:  However, the average impact reveals a peculiar threshold effect: the scientific output of a country may reach an impact larger than the world average only if the country invests more than 120 ,000 USD per researcher annually .
Edit intent: fluency
Original:  We link them to decorated hypertrees after a general study on decorated hypertrees, which we enumerate using box trees. ----- C . Jensen, J. McCammond et J. Meier ont utilis\'e des hyperarbres pond\'er\'es pour calculer la caract\'eristique d'Euler d'un sous-groupe du groupe des automorphismes d'un produit libre.
Revised:  We link them to decorated hypertrees after a general study on decorated hypertrees, which we enumerate using box trees. ---C . Jensen, J. McCammond et J. Meier ont utilis\'e des hyperarbres pond\'er\'es pour calculer la caract\'eristique d'Euler d'un sous-groupe du groupe des automorphismes d'un produit libre.
Edit intent: fluency
Original: This article discusses an efficient implementation of tensors of arbitrary rank that can be used as a basic building block for high-performance computing through the use of some of the C++ paradigms introduced by the new C++  11 requirements of the standard library.
Revised: This article discusses an efficient implementation of tensors of arbitrary rank by using some of the C++ paradigms introduced by the new C++ 11 requirements of the standard library.
Edit intent: clarity
Original: This article discusses an efficient implementation of tensors of arbitrary rank that can be used as a basic building block for high-performance computing through the use of some of the C++ paradigms introduced by the new C++  11 requirements of the standard library.
Revised: This article discusses an efficient implementation of tensors of arbitrary rank that can be used as a basic building block for high-performance computing through the use of some of the idioms introduced by the new C++ 11 requirements of the standard library.
Edit intent: clarity
Original: This article discusses an efficient implementation of tensors of arbitrary rank that can be used as a basic building block for high-performance computing through the use of some of the C++ paradigms introduced by the new C++  11 requirements of the standard library.
Revised: This article discusses an efficient implementation of tensors of arbitrary rank that can be used as a basic building block for high-performance computing through the use of some of the C++ paradigms introduced by the recently published C++ 11 requirements of the standard library.
Edit intent: clarity
Original:  By using templates, an extra high-level layer can be added to the C++ language when dealing with algebraic objects and their operations, without compromising performance.
Revised:  By using templates, an extra high-level layer is added to the C++ language when dealing with algebraic objects and their operations, without compromising performance.
Edit intent: clarity
Original: Whenever customers' choices (e.g. to buy or not a given good) depend on others choices (cases coined 'positive externalities' or 'bandwagon effect' in the economic literature), the demand may be multiply valued: for a same posted price, there is either a small number of buyers, or a large one -- in which case one says that the customers %DIFDELCMD < {\it %%% coordinate .
Revised: Whenever customers' choices (e.g. to buy or not a given good) depend on others choices (cases coined 'positive externalities' or 'bandwagon effect' in the economic literature), the demand may be multiply valued: for a same posted price, there is either a small number of buyers, or a large one -- in which case one says that the customers %DIFDELCMD < {\it %%% coordinate .
Edit intent: fluency
Original:  For estimating PVE , we demonstrate that BSLMM combines the advantages of both standard LMMs and sparse regression modeling.
Revised:  For PVE estimation , we demonstrate that BSLMM combines the advantages of both standard LMMs and sparse regression modeling.
Edit intent: clarity
Original:  It was shown in 1978 that Node Kayles,  in which players vie to chose an independent set in a graph , is PSPACE-complete.
Revised:  It was shown in 1978 that Node Kayles, a PSPACE-complete game in which players vie to chose an independent set in a graph , is PSPACE-complete.
Edit intent: clarity
Original: In this paper we present a new analysis of energy consumption in cellular network and we focus on the distribution of energy consumed by a base station  .
Revised: In this paper we present a new analysis of energy consumption in cellular networks. We focus on the distribution of energy consumed by a base station .
Edit intent: coherence
Original:  We first define the energy consumption model , in which the consumed energy is divided into two parts: the additive part and the broadcast part.
Revised:  We first define the energy consumption model in which the consumed energy is divided into two parts: the additive part and the broadcast part.
Edit intent: fluency
Original:  We first define the energy consumption model , in which the consumed energy is divided into two parts: the additive part and the broadcast part.
Revised:  We first define the energy consumption model , in which the consumed energy is divided into two parts: The additive part and the broadcast part.
Edit intent: fluency
Original:  The first one is to dimension cell radius in the economical point of view and the second one is to dimension cell battery in the sites that do not have access to electricity .
Revised:  The first one is to dimension cell radius in the economical point of view , the second one is to dimension cell battery in the sites that do not have access to electricity .
Edit intent: fluency
Original:  The first one is to dimension cell radius in the economical point of view and the second one is to dimension cell battery in the sites that do not have access to electricity .
Revised:  The first one is to dimension cell radius in the economical point of view and the second one is to dimension cell battery in the sites that do not have access to permanent power supply .
Edit intent: clarity
Original: We propose two scheduling algorithms that seek to optimize the perceptual quality of scalably coded videos transmitted over slow fading wireless channels.
Revised: We propose two scheduling algorithms that seek to optimize the quality of scalably coded videos transmitted over slow fading wireless channels.
Edit intent: clarity
Original:  Based on the MDP formulation, a near-optimal scheduling policy is computed that maximizes an objective proxy of video quality, the time-average%DIFDELCMD < {\em %%% Multi-Scale Structural SIMilarity (MS-SSIM) index.
Revised:  Based on the MDP formulation, a near-optimal scheduling policy is computed that %DIFDELCMD < {\em %%% Multi-Scale Structural SIMilarity (MS-SSIM) index.
Edit intent: clarity
Original:  Based on the MDP formulation, a near-optimal scheduling policy is computed that maximizes an objective proxy of video quality, the time-average%DIFDELCMD < {\em %%% Multi-Scale Structural SIMilarity (MS-SSIM) index.
Revised:  Based on the MDP formulation, a near-optimal scheduling policy is computed that maximizes an objective proxy of video quality, the time-average%DIFDELCMD < {\em %%% (MS-SSIM) index.
Edit intent: clarity
Original:  Using sights token from the development of the optimal MDP-based scheduling policy, the second proposed scheduling algorithm is an online scheduling method that only requires only easily measurable knowledge of the channel dynamics, and is thus viable in practice.
Revised:  Using sights token from the development of the optimal MDP-based scheduling policy, the second proposed scheduling algorithm is an online scheduling method that only requires easily measurable knowledge of the channel dynamics, and is thus viable in practice.
Edit intent: fluency
Original:  These values  rely on measures of the first two moments of the offspring distribution.
Revised:  These values ultimately rely on measures of the first two moments of the offspring distribution.
Edit intent: clarity
Original:  We discuss these bounds, focusing on the theory of s-convex ordering of random variables, a method primarily used in the field of actuarial sciences.
Revised:  We examine these bounds, focusing on the theory of s-convex ordering of random variables, a method primarily used in the field of actuarial sciences.
Edit intent: clarity
Original:  This method can be used to generate "worst case scenario" distributions using the first few moments of the offspring distribution , which then lead to upper bounds on the probability of extinction  .
Revised:  This method utilizes the first few moments of the offspring distribution , which then lead to upper bounds on the probability of extinction .
Edit intent: clarity
Original:  We examine these bounds , focusing on the theory of s-convex ordering of random variables, a method primarily used in the field of actuarial sciences.
Revised:  We examine these bounds , focusing on s-convex ordering of random variables, a method primarily used in the field of actuarial sciences.
Edit intent: clarity
Original:  This method utilizes the first few moments of the offspring distribution to generate " worst case" and " best case" distributions, which can then be used to find bounds on the probability of extinction.
Revised:  This method utilizes the first few moments of the offspring distribution to generate " best case" and " best case" distributions, which can then be used to find bounds on the probability of extinction.
Edit intent: fluency
Original:  This method utilizes the first few moments of the offspring distribution to generate " worst case" and " best case" distributions, which can then be used to find bounds on the probability of extinction.
Revised:  This method utilizes the first few moments of the offspring distribution to generate " worst case" and " worst case" distributions, which can then be used to find bounds on the probability of extinction.
Edit intent: fluency
Original:  This method utilizes the first few moments of the offspring distribution to generate " worst case" and " best case" distributions, which can then be used to find bounds on the probability of extinction.
Revised:  This method utilizes the first few moments of the offspring distribution to generate " worst case" and " best case" scenarios to provide upper and lower bounds on the probability of extinction.
Edit intent: clarity
Original:  We discuss how this approach can provide insight into the evolutionary process .
Revised:  Our results demonstrate that even the most fit strategies can have high probabilities of extinction .
Edit intent: clarity
Original: In this paper, we first investigate the problem of cooperative relay in CR networks for further enhanced network performance.
Revised: In this paper, we investigate the problem of cooperative relay in CR networks for further enhanced network performance.
Edit intent: coherence
Original: Motivated by the problem of decentralized direction-tracking , we consider the general problem of cooperative learning in multi-agent systems with time-varying connectivity and intermittent measurements.
Revised: Motivated by the problem of tracking a direction in a decentralized way , we consider the general problem of cooperative learning in multi-agent systems with time-varying connectivity and intermittent measurements.
Edit intent: clarity
Original:  Our protocol is completely distributed and able to cope with the time-varying, unpredictable  nature of inter-agent connectivity, repeated failures of nodes, and intermittent noisy measurements of \mu.
Revised:  Our protocol is completely distributed and able to cope with the time-varying, unpredictable nature of inter-agent communication, and intermittent noisy measurements of \mu.
Edit intent: clarity
Original:  Our main results bound the learning speed of our protocol in terms of a novel measure of graph connectivity we call the sieve constant of a graph .
Revised:  Our main result bounds the learning speed of our protocol in terms of a novel measure of graph connectivity we call the sieve constant of a graph .
Edit intent: fluency
Original: We study the problem of obtaining efficient, deterministic , black-box polynomial identity testing  (PIT) algorithms for read-once oblivious algebraic branching programs (ABPs)  .
Revised: We study the problem of obtaining deterministic black-box polynomial identity testing (PIT) algorithms for read-once oblivious algebraic branching programs (ABPs) .
Edit intent: clarity
Original: We study the problem of obtaining efficient, deterministic , black-box polynomial identity testing  (PIT) algorithms for read-once oblivious algebraic branching programs (ABPs)  .
Revised: We study the problem of obtaining efficient, deterministic , black-box polynomial identity testing algorithms (PIT) algorithms for read-once oblivious algebraic branching programs (ABPs) .
Edit intent: fluency
Original: We study the problem of obtaining efficient, deterministic , black-box polynomial identity testing  (PIT) algorithms for read-once oblivious algebraic branching programs (ABPs)  .
Revised: We study the problem of obtaining efficient, deterministic , black-box polynomial identity testing (PIT) for algebraic branching programs (ABPs) .
Edit intent: clarity
Original:  This class has an efficient, deterministic , white-box polynomial identity testing algorithm (due to Raz and Shpilka), but prior to this work had no known such black-box algorithm.
Revised:  This class has an deterministic white-box polynomial identity testing algorithm (due to Raz and Shpilka), but prior to this work had no known such black-box algorithm.
Edit intent: clarity
Original:  This class has an efficient, deterministic , white-box polynomial identity testing algorithm (due to Raz and Shpilka), but prior to this work had no known such black-box algorithm.
Revised:  This class has an efficient, deterministic , white-box polynomial identity testing algorithm (due to Raz and Shpilka), but prior to this work there was no known such black-box algorithm.
Edit intent: clarity
Original:  We also show that several other circuit classes can be black-box reduced to read-once oblivious ABPs, including set-multilinear ABPs (a generalization of depth 3 set-multilinear formulas), non-commutative ABPs (generalizing non-commutative formulas), and (semi-)diagonal depth-4 circuits (as introduced by Saxena , and recently shown by Mulmuley to have implications for derandomizing Noether's Normalization Lemma).
Revised:  We also show that several other circuit classes can be black-box reduced to read-once oblivious ABPs, including set-multilinear ABPs (a generalization of depth-3 set-multilinear formulas), non-commutative ABPs (generalizing non-commutative formulas), and (semi-)diagonal depth-4 circuits (as introduced by Saxena , and recently shown by Mulmuley to have implications for derandomizing Noether's Normalization Lemma).
Edit intent: fluency
Original: The scarcity of water characterizing drylands forces vegetation to adopt appropriate survival strategies.
Revised: The scarcity of water characterising drylands forces vegetation to adopt appropriate survival strategies.
Edit intent: fluency
Original:  Such models disregard the discrete nature of plant individuals and their intrinsically stochastic behaviour.
Revised:  However, although plants are usually quite plastic they also display discrete qualities and stochastic behaviour.
Edit intent: clarity
Original:  These features  give rise to demographic noise, which  can influence the qualitative dynamics of ecosystem models.
Revised:  These features may give rise to demographic noise, which can influence the qualitative dynamics of ecosystem models.
Edit intent: clarity