wanyu/IteraTeR_v2 huggingface dataset:
Original:  These problems generalize  purely robust instances of the problem , namelymax-min submodular fair allocation (SFA) and \emph{min-max submodular load balancing (SLB) , and also average-case instances , that is the submodular welfare problem (SWP) and \emph{submodular multiway partition (SMP).
Revised:  These problems generalize purely robust instances of the problem , namely(namely max-min submodular fair allocation (SFA) and \emph{min-max submodular load balancing (SLB) , and also average-case instances , that is the submodular welfare problem (SWP) and \emph{submodular multiway partition (SMP).
Edit intent: clarity
Original:  These problems generalize  purely robust instances of the problem , namelymax-min submodular fair allocation (SFA) and \emph{min-max submodular load balancing (SLB) , and also average-case instances , that is the submodular welfare problem (SWP) and \emph{submodular multiway partition (SMP).
Revised:  These problems generalize purely robust instances of the problem , namelymax-min submodular fair allocation (SFA) and \emph{min-max submodular load balancing (SLB) , and also average-case instances , that is the submodular welfare problem (SWP) and \emph{submodular multiway partition (SMP).
Edit intent: fluency
Original:  These problems generalize  purely robust instances of the problem , namelymax-min submodular fair allocation (SFA) and \emph{min-max submodular load balancing (SLB) , and also average-case instances , that is the submodular welfare problem (SWP) and \emph{submodular multiway partition (SMP).
Revised:  These problems generalize purely robust instances of the problem , namelymax-min submodular fair allocation (SFA) and \emph{min-max submodular load balancing (SLB) and also generalize average-case instances , that is the submodular welfare problem (SWP) and \emph{submodular multiway partition (SMP).
Edit intent: fluency
Original:  These problems generalize  purely robust instances of the problem , namelymax-min submodular fair allocation (SFA) and \emph{min-max submodular load balancing (SLB) , and also average-case instances , that is the submodular welfare problem (SWP) and \emph{submodular multiway partition (SMP).
Revised:  These problems generalize purely robust instances of the problem , namelymax-min submodular fair allocation (SFA) and \emph{min-max submodular load balancing (SLB) , and also average-case instances ( that is the submodular welfare problem (SWP) and \emph{submodular multiway partition (SMP).
Edit intent: fluency
Original:  While the robust versions have been studied in the theory community, existing work has focused on tight approximation guarantees, and the resultant algorithms are not generally scalable to large real-world applications.
Revised:  While the robust versions have been studied in the theory community, existing work has focused on tight approximation guarantees, and the resultant algorithms are not , in general, scalable to very large real-world applications.
Edit intent: clarity
Original:  In the present paper, we bridge this gap, by proposing several new algorithms (including  greedy, majorization-minimization, minorization-maximization, and relaxation algorithms) that not only scale to large datasets but that also achieve theoretical approximation guarantees comparable to the state-of-the-art .
Revised:  In the present paper, we bridge this gap, by proposing several new algorithms (including those based on greedy, majorization-minimization, minorization-maximization, and relaxation algorithms) that not only scale to large datasets but that also achieve theoretical approximation guarantees comparable to the state-of-the-art .
Edit intent: clarity
Original:  In the present paper, we bridge this gap, by proposing several new algorithms (including  greedy, majorization-minimization, minorization-maximization, and relaxation algorithms) that not only scale to large datasets but that also achieve theoretical approximation guarantees comparable to the state-of-the-art .
Revised:  In the present paper, we bridge this gap, by proposing several new algorithms (including greedy, majorization-minimization, minorization-maximization, and relaxation algorithms) that not only scale to large sizes but that also achieve theoretical approximation guarantees comparable to the state-of-the-art .
Edit intent: clarity
Original:  In the present paper, we bridge this gap, by proposing several new algorithms (including  greedy, majorization-minimization, minorization-maximization, and relaxation algorithms) that not only scale to large datasets but that also achieve theoretical approximation guarantees comparable to the state-of-the-art .
Revised:  In the present paper, we bridge this gap, by proposing several new algorithms (including greedy, majorization-minimization, minorization-maximization, and relaxation algorithms) that not only scale to large datasets but that also achieve theoretical approximation guarantees close to the state-of-the-art .
Edit intent: clarity
Original:  Furthermore, unfolding and refolding of the domain significantly slows the domain opening and closing rates of cCaM , a distinct scenario which can potentially influence the mechanism of calcium binding to each domain.
Revised:  Furthermore, unfolding and refolding of the domain significantly slows the domain opening and closing rates of cCaM . This potentially influences the mechanism of calcium binding to each domain.
Edit intent: coherence
Original: Fungal mycelia potentially violate each of the tenets that define individuality in paradigmatic organisms: the mycelium of a filamentous fungi can contain millions of genetically diverse  nuclei, each capable of founding new mycelia.
Revised: It is challenging to apply the tenets of individuality to filamentous fungi: a fungal mycelium can contain millions of genetically diverse nuclei, each capable of founding new mycelia.
Edit intent: clarity
Original:  Moreover a single mycelium can potentially stretch over kilometers and it unlikely that distant parts of these ultra-large mycelia share resources or have the same fitness.
Revised:  Moreover a single mycelium can potentially stretch over kilometers and it is unlikely that its distant parts share resources or have the same fitness.
Edit intent: clarity
Original:  Here we directly measure how a single mycelium of the model ascomycete Neurospora crassa {\it  is patterned into reproductive individuals, by analyzing the genetic diversity of thousands of asexual spores to determine the size of the nuclear sub-population that produces each spore.
Revised:  Here we directly measure how a single mycelium of the model ascomycete {\it is patterned into reproductive individuals, by analyzing the genetic diversity of thousands of asexual spores to determine the size of the nuclear sub-population that produces each spore.
Edit intent: clarity
Original:  Here we directly measure how a single mycelium of the model ascomycete Neurospora crassa {\it  is patterned into reproductive individuals, by analyzing the genetic diversity of thousands of asexual spores to determine the size of the nuclear sub-population that produces each spore.
Revised:  Here we directly measure how a single mycelium of the model ascomycete Neurospora crassa {\it Neurospora crassa is patterned into reproductive individuals, by analyzing the genetic diversity of thousands of asexual spores to determine the size of the nuclear sub-population that produces each spore.
Edit intent: fluency
Original:  Our data show that the size of fungal individuals is a dynamic and environment-dependent property, even within apparently totally connected fungal mycelia.
Revised:  Our data show that the size of reproductive individuals is a dynamic and environment-dependent property, even within apparently totally connected fungal mycelia.
Edit intent: clarity
Original: This paper develops a simple game theoretical network model for social media (e.g., Twitter) as opposed to social networks(e. g., Facebook).
Revised: We introduce a simple network formation model for social media (e.g., Twitter) as opposed to social networks(e. g., Facebook).
Edit intent: clarity
Original:  In our directed model, connecting to other agents has a cost, and reaching  other agents via (short ) directed paths has a benefit;
Revised:  In our directed model, connecting to other agents has a cost, and reaching other agents via short directed paths has a benefit;
Edit intent: fluency
Original:  in effect, a user wants to have information diffused to them quicklyfrom a specific set of agents , but without the cost of directly following each and every one.
Revised:  in effect, an agent wants to reach others quickly , but without the cost of directly following each and every one.
Edit intent: clarity
Original:  in effect, a user wants to have information diffused to them quicklyfrom a specific set of agents , but without the cost of directly following each and every one.
Revised:  in effect, a user wants to have information diffused to them quicklyfrom a specific set of agents , but without the cost of directly connecting each and every one.
Edit intent: clarity
Original:  moreover the set of stable networks that can be sinks of the dynamics support complex structures .
Revised:  moreover the set of fixed points of the dynamics support complex structures .
Edit intent: clarity
Original:  Here we study the effect of the link order on linear synchronisation dynamics.
Revised:  Here we study the effect of the link order on linear coordination (i.e., synchronisation) dynamics.
Edit intent: clarity
Original:  We show that the synchronisation speed considerably depends on specific orders of links.
Revised:  We show that the coordination speed considerably depends on specific orders of links.
Edit intent: clarity
Original:  In addition, applying each single link for a long time to ensure strong pairwise synchronisation before moving to a next pair of individuals does not often enhance synchronisation of the entire network.
Revised:  In addition, applying each single link for a long time to ensure strong pairwise coordination before moving to a next pair of individuals does not often enhance synchronisation of the entire network.
Edit intent: clarity
Original:  In addition, applying each single link for a long time to ensure strong pairwise synchronisation before moving to a next pair of individuals does not often enhance synchronisation of the entire network.
Revised:  In addition, applying each single link for a long time to ensure strong pairwise synchronisation before moving to a next pair of individuals does not often enhance coordination of the entire network.
Edit intent: clarity
Original:  We also implement a simple greedy algorithm to optimise the link order in favour of fast synchronisation .
Revised:  We also implement a simple greedy algorithm to optimise the link order in favour of fast coordination .
Edit intent: clarity
Original:  Price trajectories are d-dimensional continuous functions whose pathwise quadratic variations and covariations are determined by a given local-volatility matrix.
Revised:  Price trajectories are d-dimensional continuous functions whose pathwise quadratic variations and covariations are determined by a given local volatility matrix.
Edit intent: fluency
Original:  The existence of Delta hedging strategies in this pathwise setting is established via an existence result for a recursive scheme of parabolic Cauchy problems  .
Revised:  The existence of Delta hedging strategies in this pathwise setting is established via existence results for recursive schemes of parabolic Cauchy problems .
Edit intent: clarity
Original:  Our main result establishes the nonexistence of pathwise arbitrage opportunities in a class of strategies containing these Delta hedging strategies and under relatively mild conditions on the local-volatility matrix.
Revised:  Our main results establish the nonexistence of pathwise arbitrage opportunities in a class of strategies containing these Delta hedging strategies and under relatively mild conditions on the local-volatility matrix.
Edit intent: fluency
Original:  Our main result establishes the nonexistence of pathwise arbitrage opportunities in a class of strategies containing these Delta hedging strategies and under relatively mild conditions on the local-volatility matrix.
Revised:  Our main result establishes the nonexistence of pathwise arbitrage opportunities in classes of strategies containing these Delta hedging strategies and under relatively mild conditions on the local-volatility matrix.
Edit intent: fluency
Original:  Our main result establishes the nonexistence of pathwise arbitrage opportunities in a class of strategies containing these Delta hedging strategies and under relatively mild conditions on the local-volatility matrix.
Revised:  Our main result establishes the nonexistence of pathwise arbitrage opportunities in a class of strategies containing these Delta hedging strategies and under relatively mild conditions on the local volatility matrix.
Edit intent: fluency
Original:  We illustrate that, in addition to the magnitude and duration of the input stimulus, frequency of the stimulus plays a critical role in determining long-term potentiation of the MTJ. Such MTJ synaptic memory arrays can be utilized to create compact and ultra-low power intelligent neural systems.
Revised:  We illustrate that, in addition to the magnitude and duration of the input stimulus, frequency of the stimulus plays a critical role in determining long-term potentiation of the MTJ. Such MTJ synaptic memory arrays can be utilized to create compact , ultra-fast and low power intelligent neural systems.
Edit intent: clarity
Original: A right ideal (left ideal, two-sided ideal) is a non-empty language L over an alphabet \Sigma that satisfies L=L\Sigma^* (L=\Sigma^*L, L=\Sigma^*L\Sigma^*).
Revised: A right ideal (left ideal, two-sided ideal) is a non-empty language L over an alphabet \Sigma such that L=L\Sigma^* (L=\Sigma^*L, L=\Sigma^*L\Sigma^*).
Edit intent: clarity
Original:  Our work is motivated by an interest in constructing a protein-protein interaction network that captures key features associated with Parkinson's disease.
Edit intent: coherence
Original:  The proposed method is based on a Monte Carlo approach.
Revised:  The proposed method uses a Monte Carlo approach.
Edit intent: clarity
Original:  As different seed lists can give rise to the same subnetwork, we control for redundancy by choosing a minimal seed list as  starting point for the significance test.
Revised:  As different seed lists can give rise to the same subnetwork, we control for redundancy by constructing a minimal seed list as starting point for the significance test.
Edit intent: clarity
Original:  As different seed lists can give rise to the same subnetwork, we control for redundancy by choosing a minimal seed list as  starting point for the significance test.
Revised:  As different seed lists can give rise to the same subnetwork, we control for redundancy by choosing a minimal seed list as the starting point for the significance test.
Edit intent: fluency
Original:  The null model is based on random seed lists of  same length as a minimum seed list which generates the subnetwork;
Revised:  The null model is based on random seed lists of the same length as a minimum seed list which generates the subnetwork;
Edit intent: fluency
Original:  The null model is based on random seed lists of  same length as a minimum seed list which generates the subnetwork;
Revised:  The null model is based on random seed lists of same length as a minimum seed list that generates the subnetwork;
Edit intent: fluency
Original:  in this random seed list the nodes have approximately the same degree distribution as the nodes in the minimum seed list.
Revised:  in this random seed list the nodes have (approximately) the same degree distribution as the nodes in the minimum seed list.
Edit intent: fluency
Original:  We use this null model to select subnetworks which significantly deviate from random on an appropriate set of statistics and hence make suggestions as to which of the many network sampling methods might capture useful information for a real world protein-protein interaction network.
Revised:  We use this null model to select subnetworks which significantly deviate from random on an appropriate set of statistics and might capture useful information for a real world protein-protein interaction network.
Edit intent: coherence
Original:  The null model is based on random seed lists of the same length as a minimum seed list that generates the subnetwork ;
Revised:  The null model is based on random seed lists of the same length as a minimum seed list that generates the subnetwork ,
Edit intent: fluency
Original:  Neural data is often represented as a neural code: a set of binary firing patterns C\subset\{0, 1\{\it   maps between neural codes to notions of homomorphism between the corresponding neural rings.
Revised:  Neural data is often represented as a neural code: a set of binary firing patterns C\subset\{0, 1\{\it maps between neural codes and the associated homomorphisms of their neural rings.
Edit intent: clarity
Original: In the most general terms, Darwinian evolution is a flow in the space of fitness  distributions.
Revised: Darwinian evolution can be modeled in general terms as a flow in the space of fitness distributions.
Edit intent: clarity
Original:  In the limit where mutations are infinitely frequent and have infinitely small fitness effects (the "diffusion approximation" , Tsimring et al. have showed that this flow admits "fitness wave" solutions: Gaussian-shape fitness distributions moving towards higher fitness values at constant speed.
Revised:  In the diffusion approximation , Tsimring et al. have showed that this flow admits "fitness wave" solutions: Gaussian-shape fitness distributions moving towards higher fitness values at constant speed.
Edit intent: clarity
Original:  In particular, the policy depends on the distribution of the energy arrival process only through its mean and  achieves the optimal long-term average throughput of the channel within a constant gap . Existing heuristics for online power control fail to achieve such universal performance.
Revised:  In particular, the policy depends on the distribution of the energy arrival process only through its mean and it achieves the optimal long-term average throughput of the channel within a constant gap . Existing heuristics for online power control fail to achieve such universal performance.
Edit intent: clarity
Original:  This result also allows us to obtain a simple constant-gap approximation for the long-term average throughput of the system  , which sheds some light on the qualitative behavior of the throughput, namely how it depends on the distribution of the energy arrivals and the size of the battery.
Revised:  This result also allows us to approximate the long-term average throughput of the system , which sheds some light on the qualitative behavior of the throughput, namely how it depends on the distribution of the energy arrivals and the size of the battery.
Edit intent: clarity
Original:  Our results can be reformulated in terms of the functions computed by processors, and one consequence is that any increasing function from N^k to N^l that is the sum of a linear function and a periodic function can be expressed in terms of  floors of quotients by integers , and addition .
Revised:  Our results can be reformulated in terms of the functions computed by processors, and one consequence is that any increasing function from N^k to N^l that is the sum of a linear function and a periodic function can be expressed in terms of floors of quotients by integers .
Edit intent: coherence
Original: In this paper we look at the problem of minimizing regret in discounted-sum games  .
Revised: In this paper , we study the problem of minimizing regret in discounted-sum games .
Edit intent: clarity
Original:  Recently, it has been proposed that efficient stochastic solvers can be obtained via appropriately configured spiking neural networks performing Markov Chain Monte Carlo (MCMC) sampling.
Revised:  Recently, it has been proposed that efficient stochastic solvers can be obtained through appropriately configured spiking neural networks performing Markov Chain Monte Carlo (MCMC) sampling.
Edit intent: fluency
Original:  The possibility to run such models on massively parallel, low-power , neuromorphic hardware holds great promise;
Revised:  The possibility to run such models on massively parallel, low-power neuromorphic hardware holds great promise;
Edit intent: fluency
Original:  however, previously proposed networks are based on probabilistic spiking neurons, and thus rely on random number generators or external sources of noise to achieve the necessary stochasticity, leading to significant overhead in the implementation.
Revised:  however, previously proposed networks are based on probabilistically spiking neurons, and thus rely on random number generators or external sources of noise to achieve the necessary stochasticity, leading to significant overhead in the implementation.
Edit intent: fluency
Original:  however, previously proposed networks are based on probabilistic spiking neurons, and thus rely on random number generators or external sources of noise to achieve the necessary stochasticity, leading to significant overhead in the implementation.
Revised:  however, previously proposed networks are based on probabilistic spiking neurons, and thus rely on random number generators or external noise sources to achieve the necessary stochasticity, leading to significant overhead in the implementation.
Edit intent: fluency
Original:  We present an efficient implementation of spike-based CSP solvers implemented on a reconfigurable neural network VLSI device, which exploits the device's intrinsic noise sources.
Revised:  We present an efficient implementation of spike-based CSP solvers using a reconfigurable neural network VLSI device, which exploits the device's intrinsic noise sources.
Edit intent: clarity
Original:  We present an efficient implementation of spike-based CSP solvers implemented on a reconfigurable neural network VLSI device, which exploits the device's intrinsic noise sources.
Revised:  We present an efficient implementation of spike-based CSP solvers implemented on a reconfigurable neural network VLSI device, and the device's intrinsic noise sources.
Edit intent: coherence
Original: We consider a degree-corrected planted-partition model: a random graph on n nodes with two  equal-sized clusters.
Revised: We consider a Degree-Corrected Planted-Partition model: a random graph on n nodes with two equal-sized clusters.
Edit intent: fluency
Original: We consider a Degree-Corrected Planted-Partition model : a random graph on n nodes with two^n (possibly heavy-tailed), partitioned into q \geq 2 } asymptotically equal-sized clusters.
Revised: We consider the Degree-Corrected Planted-Partition model : a random graph on n nodes with two^n (possibly heavy-tailed), partitioned into q \geq 2 } asymptotically equal-sized clusters.
Edit intent: fluency
Original:  The model parameters are two constants a,b > 0 and an i.i.d. sequence of weights (\phi_u)_{u=1 finite second moment  \Phi^{(2)}.
Revised:  The model parameters are two constants a,b > 0 and the finite second moment \Phi^{(2)}.
Edit intent: clarity
Original:  Vertices u and v are joined by an edge with probability \phi_u \phi_v{n}a when they are in the same class and with probability \phi_u \phi_v{n}b otherwise.
Revised:  Vertices u and v are connected by an edge with probability \phi_u \phi_v{n}a when they are in the same class and with probability \phi_u \phi_v{n}b otherwise.
Edit intent: clarity
Original:  We prove that it is information-theoretically impossible to estimate the spins in a way positively correlated with the true community structure when (a-b)^2 \Phi^{(2)} \leq 2 (a+b).
Revised:  We prove that it is information-theoretically impossible to estimate the spins in a way positively correlated with the true community structure when (a-b)^2 \Phi^{(2)} \leq q (a+b).
Edit intent: clarity