wanyu/IteraTeR_v2 huggingface dataset:
Original:  By reversing the Turing-instability definition, the stability conditions of the considered discrete diffusive system carried out and are noted to depend upon the local dynamics of the metapopulations and the network connectivityi.e., the Fielder value of the Laplacian matrix of the graph.
Revised:  By reversing the Turing-instability idea the stability conditions of the considered discrete diffusive system carried out and are noted to depend upon the local dynamics of the metapopulations and the network connectivityi.e., the Fielder value of the Laplacian matrix of the graph.
Edit intent: clarity
Original:  By reversing the Turing-instability definition, the stability conditions of the considered discrete diffusive system carried out and are noted to depend upon the local dynamics of the metapopulations and the network connectivityi.e., the Fielder value of the Laplacian matrix of the graph.
Revised:  By reversing the Turing-instability definition, the stability conditions of the partitioned system are found to depend on local dynamics of the metapopulations and the network connectivityi.e., the Fielder value of the Laplacian matrix of the graph.
Edit intent: clarity
Original:  By reversing the Turing-instability definition, the stability conditions of the considered discrete diffusive system carried out and are noted to depend upon the local dynamics of the metapopulations and the network connectivityi.e., the Fielder value of the Laplacian matrix of the graph.
Revised:  By reversing the Turing-instability definition, the stability conditions of the considered discrete diffusive system carried out and are noted to depend upon the local dynamics of the metapopulations and the i.e., the Fielder value of the Laplacian matrix of the graph.
Edit intent: clarity
Original:  By reversing the Turing-instability definition, the stability conditions of the considered discrete diffusive system carried out and are noted to depend upon the local dynamics of the metapopulations and the network connectivityi.e., the Fielder value of the Laplacian matrix of the graph.
Revised:  By reversing the Turing-instability definition, the stability conditions of the considered discrete diffusive system carried out and are noted to depend upon the local dynamics of the metapopulations and the network connectivity the Fielder value of the Laplacian matrix of the graph.
Edit intent: coherence
Original:  By reversing the Turing-instability definition, the stability conditions of the considered discrete diffusive system carried out and are noted to depend upon the local dynamics of the metapopulations and the network connectivityi.e., the Fielder value of the Laplacian matrix of the graph.
Revised:  By reversing the Turing-instability definition, the stability conditions of the considered discrete diffusive system carried out and are noted to depend upon the local dynamics of the metapopulations and the network connectivityi.e., Fiedler value of the Laplacian matrix of the graph.
Edit intent: clarity
Original:  In the paper, necessary and sufficient conditions on the removal of some graph edges are determined to establish the stability in the remaining graph network.
Revised:  This leads to the necessary and sufficient conditions on the removal of some graph edges are determined to establish the stability in the remaining graph network.
Edit intent: coherence
Original: There has been growing evidence that cooperative interactions and configurational rearrangements underpin protein functions.
Revised: The function of proteins arises from cooperative interactions and configurational rearrangements underpin protein functions.
Edit intent: clarity
Original:  The propagator relates the gene to the connectivity of the amino acid network and the transmission of forces through the protein.
Revised:  The propagator describes how the gene determines the connectivity of the amino acid network and the transmission of forces through the protein.
Edit intent: clarity
Original:  The propagator relates the gene to the connectivity of the amino acid network and the transmission of forces through the protein.
Revised:  The propagator relates the gene to the connectivity of the amino acids, and thereby the transmission of forces through the protein.
Edit intent: clarity
Original:  Epistasis quantifies how much the combined effect of multiple mutations departs from additivity.
Edit intent: clarity
Original:  We find that epistasis is the nonlinearity of the Green function, which corresponds to a sum over multiple scattering paths passing through the localized perturbations .
Revised:  We find that epistasis is the nonlinearity of the Green function, which can be interpreted as a sum over multiple scattering paths passing through the localized perturbations .
Edit intent: clarity
Original:  We find that epistasis is the nonlinearity of the Green function, which corresponds to a sum over multiple scattering paths passing through the localized perturbations .
Revised:  We find that epistasis is the nonlinearity of the Green function, which corresponds to a sum over multiple scattering paths .
Edit intent: clarity
Original:  We apply this mechanical framework to the simulations of protein evolution, and observe long-range epistasis which facilitates collective functional modes .
Revised:  We apply this mechanical framework to simulations of protein evolution, and observe long-range epistasis which facilitates collective functional modes .
Edit intent: fluency
Original:  The underlying signal transduction mechanism produces directed motion through a bilobe response function which relates the clockwise bias of the flagellar motor to temporal changes in the attractant concentration.
Revised:  The underlying signal transduction mechanism produces directed motion through a bi-lobed response function which relates the clockwise bias of the flagellar motor to temporal changes in the attractant concentration.
Edit intent: fluency
Original:  The method allows us to calculate quantities such as the effective diffusion coefficient and drift velocity, as well as the mean number of tumbles in a given time interval, in a power series expansion in the attractant gradient.
Revised:  The method allows us to calculate quantities such as the effective diffusion coefficient and drift velocity, in a power series expansion in the attractant gradient.
Edit intent: clarity
Original:  While such quadratic filter identification problem boils down to a non-convex fourth order polynomial minimization, we discuss identifiability conditions, propose efficient algorithms to approximate the solution and analyze their performance.
Revised:  While such quadratic filter identification problem boils down to a non-convex fourth-order polynomial minimization, we discuss identifiability conditions, propose efficient algorithms to approximate the solution and analyze their performance.
Edit intent: fluency
Original:  While such quadratic filter identification problem boils down to a non-convex fourth order polynomial minimization, we discuss identifiability conditions, propose efficient algorithms to approximate the solution and analyze their performance.
Revised:  While such quadratic filter identification problem boils down to a non-convex fourth order polynomial minimization, we discuss identifiability conditions, propose algorithms to approximate the solution and analyze their performance.
Edit intent: clarity
Original:  Finally, we introduce the optional multiplicative systems associated with positive submartingales and apply them to construct random times with given Az\'ema supermartingale.
Edit intent: coherence
Original: A generalized Schelling social segregation model is applied for the description of evolving social networks in which the  number of connections of each agent (individual) remains approximately constant in time, though may be different for different agents.
Revised: We propose two models of social segregation inspired by the Schelling model. Agents in our models interact with each other via evolving networks in which the number of connections of each agent (individual) remains approximately constant in time, though may be different for different agents.
Edit intent: clarity
Original: A generalized Schelling social segregation model is applied for the description of evolving social networks in which the  number of connections of each agent (individual) remains approximately constant in time, though may be different for different agents.
Revised: A generalized Schelling social segregation model is applied for the description of evolving social networks in which the total number of connections of each agent (individual) remains approximately constant in time, though may be different for different agents.
Edit intent: clarity
Original: A generalized Schelling social segregation model is applied for the description of evolving social networks in which the  number of connections of each agent (individual) remains approximately constant in time, though may be different for different agents.
Revised: A generalized Schelling social segregation model is applied for the description of evolving social networks in which the number of connections of each agent remains constant in time, though may be different for different agents.
Edit intent: clarity
Original:  One control parameter, \mu, reflects the condition that three individuals within the same social category have some preference to form a triad .
Revised:  One control parameter, \mu, reflects the condition that three individuals within the same social category .
Edit intent: clarity
Original:  The second parameter, \nu, controls the preference for  two individuals from different social categories to be connected .
Revised:  The second parameter, \nu, controls the preference for interactions between two individuals from different social categories to be connected .
Edit intent: clarity
Original:  The second parameter, \nu, controls the preference for  two individuals from different social categories to be connected .
Revised:  The second parameter, \nu, controls the preference for two individuals from different social categories .
Edit intent: clarity
Original:  The polychromatic model enjoys several regimes separated by phase transitions in the (\mu,\nu) parameter space.
Revised:  The polychromatic model has several distinct regimes in (\mu,\nu) parameter space.
Edit intent: clarity
Original:  The second "colorless" model describes a society in which advantage or disadvantage of forming small fully connected communities (short cycles or cliques in a graph) is controlled by a single "energy" parameter, \gamma.
Revised:  The second "colorless" model describes a society in which the advantage, or disadvantage of forming small fully connected communities (short cycles or cliques in a graph) is controlled by a single "energy" parameter, \gamma.
Edit intent: fluency
Original:  The second "colorless" model describes a society in which advantage or disadvantage of forming small fully connected communities (short cycles or cliques in a graph) is controlled by a single "energy" parameter, \gamma.
Revised:  The second "colorless" model describes a society in which advantage or disadvantage of small fully connected communities (short cycles or cliques in a graph) is controlled by a single "energy" parameter, \gamma.
Edit intent: clarity
Original:  The second "colorless" model describes a society in which advantage or disadvantage of forming small fully connected communities (short cycles or cliques in a graph) is controlled by a single "energy" parameter, \gamma.
Revised:  The second "colorless" model describes a society in which advantage or disadvantage of forming small fully connected communities (short cycles in a graph) is controlled by a single "energy" parameter, \gamma.
Edit intent: clarity
Original:  The second "colorless" model describes a society in which advantage or disadvantage of forming small fully connected communities (short cycles or cliques in a graph) is controlled by a single "energy" parameter, \gamma.
Revised:  The second "colorless" model describes a society in which advantage or disadvantage of forming small fully connected communities (short cycles or cliques in a graph) is controlled by an energy-like parameter, \gamma.
Edit intent: clarity
Original:  We analyze the topological structure of a social network in this model and demonstrate that for some critical threshold, \gamma^+>0, the entire network splits into the set of weakly connected clusters, while at another threshold, \gamma^-<0, the network acquires a bipartite graph structure.
Revised:  We analyze the topological structure of a social network and demonstrate that for some critical threshold, \gamma^+>0, the entire network splits into the set of weakly connected clusters, while at another threshold, \gamma^-<0, the network acquires a bipartite graph structure.
Edit intent: clarity
Original:  We analyze the topological structure of a social network in this model and demonstrate that for some critical threshold, \gamma^+>0, the entire network splits into the set of weakly connected clusters, while at another threshold, \gamma^-<0, the network acquires a bipartite graph structure.
Revised:  We analyze the topological structure of a social network in this model and demonstrate that for some critical threshold, \gamma^+>0, the entire network splits into a set of weakly connected clusters, while at another threshold, \gamma^-<0, the network acquires a bipartite graph structure.
Edit intent: fluency
Original:  Our results shed light on social segregation and self-organized formation of cliques in social networks .
Revised:  Our results shed light on patterns of segregation in social networks, international relations and on formation of self-organized cliques in societies .
Edit intent: clarity
Original:  Agents in our models interact with each other via evolving networks in which the total number of  connections of each agent remains constant in time, though may vary from one agent to the other.
Revised:  Agents in our models are nodes of evolving social networks. The total number of connections of each agent remains constant in time, though may vary from one agent to the other.
Edit intent: clarity
Original:  Agents in our models interact with each other via evolving networks in which the total number of  connections of each agent remains constant in time, though may vary from one agent to the other.
Revised:  Agents in our models interact with each other via evolving networks in which the total number of connections of each node remains constant in time, though may vary from one agent to the other.
Edit intent: clarity
Original:  Agents in our models interact with each other via evolving networks in which the total number of  connections of each agent remains constant in time, though may vary from one agent to the other.
Revised:  Agents in our models interact with each other via evolving networks in which the total number of connections of each agent remains constant in time, though may vary from one node to the other.
Edit intent: clarity
Original:  One parameter , \mu , favors connected "monochromatic triads", i.e. connected groups of three individuals within the same social category.
Revised:  The parameter \mu favors/disfavors connected "monochromatic triads", i.e. connected groups of three individuals within the same social category.
Edit intent: clarity
Original:  The second parameter , \nu , controls the preference for interactions between two individuals from different social categories .
Revised:  The second parameter , \nu , controls the preference of interactions between two individuals from different social categories .
Edit intent: fluency
Original:  The second parameter , \nu , controls the preference for interactions between two individuals from different social categories .
Revised:  The second parameter , \nu , controls the preference for interactions between two individuals from different social categories .
Edit intent: fluency
Original:  In \nu-dominated part of the parameter space , the phase diagram is characterized by the plateau in the number of  inter-color connections, where the network is bipartite, while in \mu-dominated region  the network looks as two weakly connected unicolor clusters.
Revised:  In \nu-dominated region , the phase diagram is characterized by the plateau in the number of inter-color connections, where the network is bipartite, while in \mu-dominated region the network looks as two weakly connected unicolor clusters.
Edit intent: clarity
Original:  In \nu-dominated part of the parameter space , the phase diagram is characterized by the plateau in the number of  inter-color connections, where the network is bipartite, while in \mu-dominated region  the network looks as two weakly connected unicolor clusters.
Revised:  In \nu-dominated part of the parameter space , the phase diagram is characterized by the plateau in the number of the inter-color connections, where the network is bipartite, while in \mu-dominated region the network looks as two weakly connected unicolor clusters.
Edit intent: fluency
Original:  In \nu-dominated part of the parameter space , the phase diagram is characterized by the plateau in the number of  inter-color connections, where the network is bipartite, while in \mu-dominated region  the network looks as two weakly connected unicolor clusters.
Revised:  In \nu-dominated part of the parameter space , the phase diagram is characterized by the plateau in the number of inter-color connections, where the network is bipartite, while in \mu-dominated region , the network looks as two weakly connected unicolor clusters.
Edit intent: fluency
Original:  At \mu>crit and \nu >\nu_{crit} two phases are separated by a critical line, while at small values of \mu and \nu, a more gradual crossover between  two phases occurs.
Revised:  At \mu>crit and \nu >\nu_{crit} two phases are separated by a critical line, while at small values of \mu and \nu, a gradual crossover between two phases occurs.
Edit intent: clarity
Original:  At \mu>crit and \nu >\nu_{crit} two phases are separated by a critical line, while at small values of \mu and \nu, a more gradual crossover between  two phases occurs.
Revised:  At \mu>crit and \nu >\nu_{crit} two phases are separated by a critical line, while at small values of \mu and \nu, a more gradual crossover between the two phases occurs.
Edit intent: fluency
Original:  The second "colorless" model describes a society in which the advantage , or disadvantage of small fully connected communities (short cycles  in a graph) is controlled by an energy-like parameter , \gamma.
Revised:  The second "colorless" model describes a society in which the advantage /disadvantage of forming small fully connected communities (short cycles in a graph) is controlled by an energy-like parameter , \gamma.
Edit intent: clarity
Original:  The second "colorless" model describes a society in which the advantage , or disadvantage of small fully connected communities (short cycles  in a graph) is controlled by an energy-like parameter , \gamma.
Revised:  The second "colorless" model describes a society in which the advantage , or disadvantage of small fully connected communities (short cycles in a graph) is controlled by a parameter \gamma.
Edit intent: clarity
Original:  We analyze the topological structure of a social network  and demonstrate that for some critical threshold, \gamma^+>0, the entire network splits into a set of weakly connected clusters, while at another threshold, \gamma^-<0, the network acquires a bipartite graph structure.
Revised:  We analyze the topological structure of a social network and demonstrate that above a critical threshold, \gamma^+>0, the entire network splits into a set of weakly connected clusters, while at another threshold, \gamma^-<0, the network acquires a bipartite graph structure.
Edit intent: clarity
Original:  We analyze the topological structure of a social network  and demonstrate that for some critical threshold, \gamma^+>0, the entire network splits into a set of weakly connected clusters, while at another threshold, \gamma^-<0, the network acquires a bipartite graph structure.
Revised:  We analyze the topological structure of a social network and demonstrate that for some critical threshold, \gamma^+>0, the entire network splits into a set of weakly connected clusters, while below another threshold, \gamma^-<0, the network acquires a bipartite graph structure.
Edit intent: clarity
Original:  Our results shed light on patterns of segregation in social networks, international relations and on formation of self-organized cliques in societies.
Revised:  Our results propose mechanisms of formation of self-organized cliques in societies.
Edit intent: clarity
Original:  Recently, the deep learning community has found that features of the VGG network trained on the ImageNet classification task has been remarkably useful as a training loss for image synthesis.
Revised:  Recently, the deep learning community has found that features of the VGG network trained on ImageNet classification has been remarkably useful as a training loss for image synthesis.
Edit intent: clarity
Original:  Here, we focus on the relationship between mobility and social behaviour by analysing two high-resolution longitudinal datasets collecting trajectories and mobile phone interactions of \sim 1000 individuals .
Revised:  Here, we focus on the relationship between mobility and social behaviour by analysing trajectories and mobile phone interactions of \sim 1000 individuals .
Edit intent: clarity
Original:  We point out that different individuals balance the exploration-exploitation trade-off in different ways and we explain part of the variability in the data by the big five personality traits.
Revised:  We show that different individuals balance the exploration-exploitation trade-off in different ways and we explain part of the variability in the data by the big five personality traits.
Edit intent: coherence
Original:  We find that, in both realms, extraversion correlates with an individual's attitude towards exploration and routine diversity, while neuroticism and openness account for the tendency to evolve routine over long time-scales.
Revised:  We point out that, in both realms, extraversion correlates with an individual's attitude towards exploration and routine diversity, while neuroticism and openness account for the tendency to evolve routine over long time-scales.
Edit intent: clarity
Original:  We find that, in both realms, extraversion correlates with an individual's attitude towards exploration and routine diversity, while neuroticism and openness account for the tendency to evolve routine over long time-scales.
Revised:  We find that, in both realms, extraversion correlates with the attitude towards exploration and routine diversity, while neuroticism and openness account for the tendency to evolve routine over long time-scales.
Edit intent: clarity
Original:  A challenge is to set prices that are appropriately smooth in space and time, in the sense that drivers will choose to accept their dispatched trips, rather than drive to another area or wait for higher prices or a better trip.
Revised:  A challenge is to set prices that are appropriately smooth in space and time, so that drivers will choose to accept their dispatched trips, rather than drive to another area or wait for higher prices or a better trip.
Edit intent: coherence
Original:  The mechanism is incentive-aligned, in that it is a subgame-perfect equilibrium for drivers to accept their dispatches, and the mechanism is  welfare-optimal, envy-free, individually rational and budget balanced from any history onward.
Revised:  The mechanism is incentive-aligned, in that it is a subgame-perfect equilibrium for drivers to accept their dispatches, and the mechanism is also welfare-optimal, envy-free, individually rational and budget balanced from any history onward.
Edit intent: clarity
Original:  The same connection to min-cost flow problems provides an efficient algorithm to compute an optimal matching and prices.
Edit intent: coherence