wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Looking at the strategy composition, we retain equilibrium stationarity in general and  stability in potential games under admissible dynamics. Local stability of an equilibrium composition under any admissible dynamic can be tested by local stability of the corresponding aggregate equilibrium under the best response dynamic with i.i.d.~payoff perturbation. All the results are maintained under heterogeneity in revision protocols .
Revised:  Looking at the strategy composition, we retain equilibrium stationarity in general and stability in potential games are extended from the homogeneous setting to the heterogeneous setting. In particular, a wide class of admissible dynamics share the same set of locally stable equilibria in a potential game through local maximization of the potential .
Edit intent: meaning-changed
Original:  We formally define net gains from revisions and obtain several general properties of the gain function, which leads to Nash stability of contractive games---generalization of concave potential games---and local asymptotic stability of a (regular ) evolutionary stable state.
Revised:  We formally define net gains from revisions and obtain several general properties of the gain function, which leads to Nash stability of contractive games---generalization of concave potential games---and local asymptotic stability of a regular evolutionary stable state.
Edit intent: fluency
Original:  The unifying framework allows us to apply the Nash stability to mixture of heterogeneous populations, whether heterogeneity is observable or unobservable or whether heterogeneity is in payoffs or in revision protocols . This extends the known positive results on evolutionary implementation of social optimum through Pigouvian pricing to the presence of heterogeneity and non-aggregate payoff perturbations .
Revised:  The unifying framework allows us to apply the Nash stability to mixture of heterogeneous populations, whether heterogeneity is observable or unobservable or whether heterogeneity is in payoffs or in revision protocols .
Edit intent: coherence
Original:  To clarify the gain from revision, we propose a framework to reconstruct an evolutionary dynamic from optimal decision with stochastic (possibly restricted) available action set and switching cost. Many major dynamics and interesting new dynamicscan be constructed in this framework. We formally define net gains from revisions and obtain several general properties of the gain function, which leads to Nash stability of contractive games---generalization of concave potential games---and local asymptotic stability of a regular evolutionary stable state. The unifying framework allows us to apply the Nash stability to mixture of heterogeneous populations, whether heterogeneity is in payoffs or in revision protocols.
Revised:  In economics, static stability is traditionally defined as a notion about how incentives respond to choices: for a population game, it means that, on average, the payoff of a strategy responds negatively to an increase in the share of the strategy. This is characterized by negative definiteness of the Hessian matrix of the payoff function and satisfied globally in a contractive game and locally at a regular ESS. We say an evolutionary dynamic is economically reasonable, if an agent's choice of a new strategy can be justified as an optimal choice possibly by introducing additional costs and constraints; for example, inertia can be justified by switching costs, and switches to suboptimal strategies can be by restriction to available strategies. This class of dynamics includes not only the best response dynamic, pairwise payoff comparison dynamics and excess payoff dynamics. The key in our proof is a net gain from revision of the strategy, i.e., the payoff improvement by the revision minus the switching cost. Static stability implies that the aggregate net gain monotonically decreases over time under an economic reasonable dynamic and thus can be used as a Lyapunov function. Our Lyapunov function allows us to apply the Nash stability to mixture of heterogeneous populations, whether heterogeneity is in payoffs or in revision protocols.
Edit intent: meaning-changed
Original:  The unifying framework allows us to apply the Nash stability to mixture of heterogeneous populations, whether heterogeneity is in payoffs or in revision protocols. While the analysis here is confined to general strategic-form games , we finally discuss that the idea of reconstructing evolutionary dynamics from optimization with switching costs and focusing on net revision gains for stability is promising for further applications to more complex situations.
Revised:  The unifying framework allows us to apply the Nash stability to mixture of heterogeneous populations, who may follow different dynamics or different payoff functions. While our analysis here is confined to general strategic-form games , we finally discuss that the idea of reconstructing evolutionary dynamics from optimization with switching costs and focusing on net revision gains for stability is promising for further applications to more complex situations.
Edit intent: clarity
Original:  In economics, static stability is traditionally defined as a notion about how incentives respond to choices : for a population game, it means that, on average, the payoff of a strategy responds negatively to an increase in the share of the strategy.
Revised:  In economics, static stability is traditionally defined by negative relationship between endogenous and exogenous variables in a model : for a population game, it means that, on average, the payoff of a strategy responds negatively to an increase in the share of the strategy.
Edit intent: meaning-changed
Original:  In economics, static stability is traditionally defined as a notion about how incentives respond to choices : for a population game, it means that, on average, the payoff of a strategy responds negatively to an increase in the share of the strategy. This is characterized by negative definiteness of the Jacobian matrix of the payoff function and satisfied globally in a contractive game and locally at a regular ESS.
Revised:  In economics, static stability is traditionally defined as a notion about how incentives respond to choices : for a population game, this is characterized by negative definiteness of the Jacobian matrix of the payoff function and satisfied globally in a contractive game and locally at a regular ESS.
Edit intent: clarity
Original:  This is characterized by negative definiteness of the Jacobian matrix of the payoff function and satisfied globally in a contractive game and locally at a regular ESS. We say an evolutionary dynamic is economically reasonable , if an agent' s choice of a new strategy can be justified as an optimal choice possibly by introducing additional costs and constraints ;
Revised:  This is characterized by negative definiteness of the Jacobian matrix of the payoff function . We consider economically reasonable dynamics, in which we can justify agents' choices of new strategies as optimal choices possibly by introducing additional costs and constraints ;
Edit intent: clarity
Original:  We say an evolutionary dynamic is economically reasonable , if an agent' s choice of a new strategy can be justified as an optimal choice possibly by introducing additional costs and constraints ; for example, inertia can be justified by switching costs, and switches to suboptimal strategies can be by restriction to available strategies .
Revised:  We say an evolutionary dynamic is economically reasonable , if an agent' s choice of a new strategy can be justified as an optimal choice possibly by introducing additional costs and constraints .
Edit intent: coherence
Original:  The key in our proof is a net gain from revision of the strategy , i.e., the payoff improvement by the revision minus the switching cost . Static stability implies that the aggregate net gain monotonically decreases over time under an economic reasonable dynamic and thus can be used as a Lyapunov function.
Revised:  The key is expected net gains (payoff improvements) from strategy revisions after paying switching costs . Static stability implies that the aggregate net gain monotonically decreases over time under an economic reasonable dynamic and thus can be used as a Lyapunov function.
Edit intent: clarity
Original:  The key in our proof is a net gain from revision of the strategy , i.e., the payoff improvement by the revision minus the switching cost . Static stability implies that the aggregate net gain monotonically decreases over time under an economic reasonable dynamic and thus can be used as a Lyapunov function.
Revised:  The key in our proof is a net gain from revision of the strategy , i.e., the payoff improvement by the revision minus the switching cost . Static stability implies that the aggregate net gain diminishes over time under an economic reasonable dynamic and thus can be used as a Lyapunov function.
Edit intent: clarity
Original:  The key in our proof is a net gain from revision of the strategy , i.e., the payoff improvement by the revision minus the switching cost . Static stability implies that the aggregate net gain monotonically decreases over time under an economic reasonable dynamic and thus can be used as a Lyapunov function.
Revised:  The key in our proof is a net gain from revision of the strategy , i.e., the payoff improvement by the revision minus the switching cost . Static stability implies that the aggregate net gain monotonically decreases over time under economic reasonable dynamics and thus can be used as a Lyapunov function.
Edit intent: fluency
Original: This paper presents a universal and economically intuitive approach to linking static and dynamic stability. In economics, static stability is traditionally defined by negative relationship between endogenous and exogenous variables in a model: for a population game , this is characterized by negative semidefiniteness of the Jacobian matrix of the payoff function. We consider economically reasonable dynamics, in which we can justify agents' choices of new strategies as optimal choices possibly by introducing additional costs and constraints .
Revised: Static stability in an economic model typically means negative incentives for deviation from equilibrium strategies, which we expect to assure a return to equilibrium, i.e., dynamic stability, as long as agents respond to incentives. There have been many attempts to prove this link, especially in evolutionary game theory, yielding both negative and positive results. This paper offers a universal and intuitive approach to this link. We prove static stability assures dynamic stability as long as agents' decisions of switching strategies are rationalizable by revealing costs and constraints .
Edit intent: clarity
Original:  We consider economically reasonable dynamics, in which we can justify agents' choices of new strategies as optimal choices possibly by introducing additional costs and constraints . This class of dynamics covers major payoff-based (non-imitative) evolutionary dynamics. The key is expected net gains (payoff improvements) from strategy revisions after paying switching costs. Static stability implies that the aggregate net gain diminishes over time under economic reasonable dynamics and thus can be used as a Lyapunov function.
Revised:  We consider economically reasonable dynamics, in which we can justify agents' choices of new strategies as optimal choices possibly by introducing additional costs and constraints behind distortions from exact optimization. This idea guides us to track the remaining expected maximal payoff gain from switches, after deducting the costs and to be maximized subject to the constraints, as a disequilibrium index, namely, a Lyapunov function.
Edit intent: clarity
Original: Development of a mesoscale neural circuitry map of the common marmoset is an essential task due to the ideal characteristics of the marmoset as a URLanism for neuroscience research .
Revised: Whole brain neuroanatomy using tera-voxel light-microscopic data sets is of much current interest. A fundamental problem in this field is the mapping of individual brain data sets to a reference space. Previous work has not rigorously quantified the distortions in brain geometry from in-vivo to ex-vivo brains due to the ideal characteristics of the marmoset as a URLanism for neuroscience research .
Edit intent: meaning-changed
Original: Development of a mesoscale neural circuitry map of the common marmoset is an essential task due to the ideal characteristics of the marmoset as a URLanism for neuroscience research .
Revised: Development of a mesoscale neural circuitry map of the common marmoset is an essential task due to the tissue processing, which will be important when computing properties such as local cell and process densities at the voxel level in creating reference brain maps. Further, existing approaches focus on registering uni-modal volumetric data; however, given the increasing interest in the marmoset model for neuroscience research .
Edit intent: meaning-changed
Original: Development of a mesoscale neural circuitry map of the common marmoset is an essential task due to the ideal characteristics of the marmoset as a URLanism for neuroscience research . To facilitate this development there is a need for new computational tools to cross-register multi-modal data sets containing MRI volumes as well as multiple histological series , and to register the combined data set to a common reference atlas.
Revised: Development of a mesoscale neural circuitry map of the common marmoset is an essential task due to the ideal characteristics of the marmoset as a URLanism for neuroscience research , it is necessary to cross-register multi-modal data sets containing MRI volumes as well as multiple histological series , and to register the combined data set to a common reference atlas.
Edit intent: coherence
Original:  To facilitate this development there is a need for new computational tools to cross-register multi-modal data sets containing MRI volumes as well as multiple histological series , and to register the combined data set to a common reference atlas.
Revised:  To facilitate this development there is a need for new computational tools to cross-register multi-modal data sets including MRIs and multiple histological series , and to register the combined data set to a common reference atlas.
Edit intent: clarity
Original:  To facilitate this development there is a need for new computational tools to cross-register multi-modal data sets containing MRI volumes as well as multiple histological series , and to register the combined data set to a common reference atlas. We present a fully automatic pipeline for same-subject-MRI guided reconstruction of image volumes from a series of histological sections of different modalities, followed by diffeomorphic mapping to a reference atlas.
Revised:  To facilitate this development there is a need for new computational tools to cross-register multi-modal data sets containing MRI volumes as well as multiple histological series that can help address individual variations in brain architecture. Here we present a computational approach for same-subject multimodal MRI guided reconstruction of image volumes from a series of histological sections of different modalities, followed by diffeomorphic mapping to a reference atlas.
Edit intent: meaning-changed
Original:  We show registration results for Nissl, myelin, CTB, and fluorescent tracer images using a same-subject ex-vivo MRI as our reference and show that our method achieves accurate registration and eliminates artifactual warping that may be result from the absence of a reference MRI data set. Examination of the determinant of the local metric tensor of the diffeomorphic mapping between each subject's ex-vivo MRI and resultant Nissl reconstruction allows an unprecedented local quantification of geometrical distortions resulting from the histological processing, showing a slight shrinkage, a median linear\pm  scale change of ~-1\% in going from the ex-vivo MRI to the tape-transfer generated histological image data\pm  .
Revised:  We quantify the scale change during the different stages of histological processing of the brains using the Jacobian determinant of the local metric tensor of the diffeomorphic mapping between each subject's ex-vivo MRI and resultant Nissl reconstruction allows an unprecedented local quantification of geometrical distortions resulting from the histological processing, showing a slight shrinkage, a median linear\pm scale change of ~-1\% in going from the ex-vivo MRI to the tape-transfer generated histological image data\pm .
Edit intent: meaning-changed
Original:  Examination of the determinant of the local metric tensor of the diffeomorphic mapping between each subject's ex-vivo MRI and resultant Nissl reconstruction allows an unprecedented local quantification of geometrical distortions resulting from the histological processing, showing a slight shrinkage, a median linear\pm  scale change of ~-1\% in going from the ex-vivo MRI to the tape-transfer generated histological image data\pm  .
Revised:  Examination of the determinant of the diffeomorphic transformations involved. There are two major steps in the histology process with associated scale distortions (a) brain perfusion (b) histological sectioning and reassembly. By mapping the final image stacks to the ex-vivo MRI and resultant Nissl reconstruction allows an unprecedented local quantification of geometrical distortions resulting from the histological processing, showing a slight shrinkage, a median linear\pm scale change of ~-1\% in going from the ex-vivo MRI to the tape-transfer generated histological image data\pm .
Edit intent: meaning-changed
Original:  Examination of the determinant of the local metric tensor of the diffeomorphic mapping between each subject's ex-vivo MRI and resultant Nissl reconstruction allows an unprecedented local quantification of geometrical distortions resulting from the histological processing, showing a slight shrinkage, a median linear\pm  scale change of ~-1\% in going from the ex-vivo MRI to the tape-transfer generated histological image data\pm  .
Revised:  Examination of the determinant of the local metric tensor of the diffeomorphic mapping between each subject's ex-vivo post fixation MRI, we show that tape-transfer histology can be reassembled accurately into 3D volumes with a local scale change of 2.0\pm scale change of ~-1\% in going from the ex-vivo MRI to the tape-transfer generated histological image data\pm .
Edit intent: meaning-changed
Original:  Examination of the determinant of the local metric tensor of the diffeomorphic mapping between each subject's ex-vivo MRI and resultant Nissl reconstruction allows an unprecedented local quantification of geometrical distortions resulting from the histological processing, showing a slight shrinkage, a median linear\pm  scale change of ~-1\% in going from the ex-vivo MRI to the tape-transfer generated histological image data\pm  .
Revised:  Examination of the determinant of the local metric tensor of the diffeomorphic mapping between each subject's ex-vivo MRI and resultant Nissl reconstruction allows an unprecedented local quantification of geometrical distortions resulting from the histological processing, showing a slight shrinkage, a median linear\pm 0.4\% per axis dimension. In contrast, the perfusion step, as assessed by mapping the in-vivo MRIs to the ex-vivo post fixation MRIs, shows a larger local scale change of ~-1\% in going from the ex-vivo MRI to the tape-transfer generated histological image data\pm .
Edit intent: meaning-changed
Original:  Examination of the determinant of the local metric tensor of the diffeomorphic mapping between each subject's ex-vivo MRI and resultant Nissl reconstruction allows an unprecedented local quantification of geometrical distortions resulting from the histological processing, showing a slight shrinkage, a median linear\pm  scale change of ~-1\% in going from the ex-vivo MRI to the tape-transfer generated histological image data\pm  .
Revised:  Examination of the determinant of the local metric tensor of the diffeomorphic mapping between each subject's ex-vivo MRI and resultant Nissl reconstruction allows an unprecedented local quantification of geometrical distortions resulting from the histological processing, showing a slight shrinkage, a median linear\pm scale change of 6.9\pm .
Edit intent: meaning-changed
Original:  Examination of the determinant of the local metric tensor of the diffeomorphic mapping between each subject's ex-vivo MRI and resultant Nissl reconstruction allows an unprecedented local quantification of geometrical distortions resulting from the histological processing, showing a slight shrinkage, a median linear\pm  scale change of ~-1\% in going from the ex-vivo MRI to the tape-transfer generated histological image data\pm  .
Revised:  Examination of the determinant of the local metric tensor of the diffeomorphic mapping between each subject's ex-vivo MRI and resultant Nissl reconstruction allows an unprecedented local quantification of geometrical distortions resulting from the histological processing, showing a slight shrinkage, a median linear\pm scale change of ~-1\% in going from the ex-vivo MRI to the tape-transfer generated histological image data\pm 2.1\% per axis dimension. This is the first systematic quantification of the local metric distortions associated with whole-brain histological processing, and we expect that the results will generalize to other species .
Edit intent: meaning-changed
Original: Clinically-relevant forms of acute cell injury, which include stroke and myocardial infarction, have been of long-lasting challenge in terms of successful intervention and treatments. Although laboratory studies have shown it is possible to decrease cell death after such injuries, human clinical trials based on laboratory therapies have generally failed. We suggested these failures are due, at least partially, to the lack of a quantitativetheoretical framework for acute cell injury.
Revised: Clinically-relevant forms of acute cell injury, such as stroke and heart attack, are of tremendous impact and have attracted huge amounts of research effort. The biomedical research that seeks cures for these conditions has been dominated by a qualitative, inductive mindset. Although the inductive approach has not been effective in developing medical treatments, it has amassed enough information to allow construction of quantitative, deductive models of acute cell injury.
Edit intent: clarity
Original:  Here we provide a systematic study on a nonlinear dynamical model of acute cell injury and characterize the global dynamics of a nonautonomous version of the theory.
Revised:  Here we provide a systematic study on a nonlinear dynamical model of acute cell injury that offered new ways to conceptualize cell injury but possessed limitations that decrease its effectiveness. Here we study the global dynamics of a nonautonomous version of the theory.
Edit intent: meaning-changed
Original:  Here we provide a systematic study on a nonlinear dynamical model of acute cell injury and characterize the global dynamics of a nonautonomous version of the theory. The nonautonomous model gives rise to four qualitative types of dynamical patterns that can be mapped to the behavior of cells after clinical acute injuries.
Revised:  Here we provide a systematic study on a nonlinear dynamical model of acute cell injury and characterize the global dynamics of the cell injury theory using a nonautonomous formulation. Different from the standard scenario in nonlinear dynamics that is determined by the steady state and fixed points of the model equations, in this nonautonomous model with a trivial fixed point, the system property is dominated by the transient states and the corresponding dynamic processes. The model gives rise to four qualitative types of dynamical patterns that can be mapped to the behavior of cells after clinical acute injuries.
Edit intent: meaning-changed