wanyu/IteraTeR_v2 huggingface dataset:
Original:  We expect the quantum information-hiding mapping approach to shed light on the understanding of fundamental connections among computational complexity and information scrambling .
Revised:  We expect the quantum information-hiding mapping approach may shed light on the understanding of fundamental connections among computational complexity and information scrambling .
Edit intent: style
Original:  In this study, we present a novel stochastic algorithm  which we call the Christmas tree algorithm (CTA)  for sequential sampling of junction trees of decomposable graphs.
Revised:  In this study, we present a novel stochastic algorithm , which we call the Christmas tree algorithm (CTA) for sequential sampling of junction trees of decomposable graphs.
Edit intent: fluency
Original:  In this study, we present a novel stochastic algorithm  which we call the Christmas tree algorithm (CTA)  for sequential sampling of junction trees of decomposable graphs.
Revised:  In this study, we present a novel stochastic algorithm which we call the Christmas tree algorithm (CTA) , for sequential sampling of junction trees of decomposable graphs.
Edit intent: fluency
Original:  In this study, we present a novel stochastic algorithm  which we call the Christmas tree algorithm (CTA)  for sequential sampling of junction trees of decomposable graphs.
Revised:  In this study, we present a novel stochastic algorithm which we call the Christmas tree algorithm (CTA) for sequential sampling of junction trees for decomposable graphs.
Edit intent: fluency
Original:  We show that , by incrementally expanding the underlying graph with one vertex at a time, the CTA is able to construct all junction trees for any given number of underlying vertices.
Revised:  We show that the CTA, expanding incrementally the underlying graph with one vertex at a time, the CTA is able to construct all junction trees for any given number of underlying vertices.
Edit intent: fluency
Original:  We show that , by incrementally expanding the underlying graph with one vertex at a time, the CTA is able to construct all junction trees for any given number of underlying vertices.
Revised:  We show that , by incrementally expanding the underlying graph with one vertex at a time, has full support on the space of junction trees with any given number of underlying vertices.
Edit intent: clarity
Original:  The relevance of our suggested algorithm is justified from a sequential Monte Carlo (SMC) perspective for approximating distributions over decomposable graphs, where the transition kernel from the CTA is employed as proposal kernel ;
Revised:  The relevance of our suggested algorithm is justified from a sequential Monte Carlo (SMC) perspective , as the CTA can be effectively employed as proposal kernel ;
Edit intent: clarity
Original:  for more details see the companion paper Olsson et al.
Revised:  for more details see the companion paper Olsson et . al
Edit intent: fluency
Original: The junction tree representation provides an attractive structural property for organizing a decomposable graph.
Revised: The junction-tree representation provides an attractive structural property for organizing a decomposable graph.
Edit intent: fluency
Original:  The relevance of our suggested algorithm is justified from a sequential Monte Carlo (SMC) perspective, as the CTA can be effectively employed as proposal kernel in SMC algorithms sampling from distributions on spaces of decomposable graphs ;
Revised:  A direct application of our suggested algorithm is justified from a sequential Monte Carlo (SMC) perspective, as the CTA can be effectively employed as proposal kernel in SMC algorithms sampling from distributions on spaces of decomposable graphs ;
Edit intent: clarity
Original:  The relevance of our suggested algorithm is justified from a sequential Monte Carlo (SMC) perspective, as the CTA can be effectively employed as proposal kernel in SMC algorithms sampling from distributions on spaces of decomposable graphs ;
Revised:  The relevance of our suggested algorithm is demonstrated in a sequential Monte Carlo (SMC) perspective, as the CTA can be effectively employed as proposal kernel in SMC algorithms sampling from distributions on spaces of decomposable graphs ;
Edit intent: clarity
Original:  The relevance of our suggested algorithm is justified from a sequential Monte Carlo (SMC) perspective, as the CTA can be effectively employed as proposal kernel in SMC algorithms sampling from distributions on spaces of decomposable graphs ;
Revised:  The relevance of our suggested algorithm is justified from a sequential Monte Carlo (SMC) perspective, as the CTA can be effectively employed as proposal kernel ;
Edit intent: clarity
Original:  The CTA kernel is a flexible idea which adapts to a variety of interesting inferential problems in probabilistic graphical models.
Edit intent: coherence
Original:  A numerical study of the SMC approximation illustrates the utility of our approach by two examples: in the first one, how the CTA can be incorporated successfully into a particle Gibbs sampler for Bayesian structure learning in decomposable graphical models;
Revised:  A numerical study illustrates the utility of our approach by two examples: in the first one, how the CTA can be incorporated successfully into a particle Gibbs sampler for Bayesian structure learning in decomposable graphical models;
Edit intent: clarity
Original:  in the second one, we provide an unbiased estimator for the number of decomposable graphs for a given number of vertices.
Revised:  in the second one, we provide an unbiased estimator of the number of decomposable graphs for a given number of vertices.
Edit intent: fluency
Original:   A direct application of our suggested algorithm is demonstrated in a sequential Monte Carlo setting designed for sampling from distributions on spaces of decomposable graphs , where the junction-tree expander can be effectively employed as proposal kernel;
Revised:  A direct application of our suggested algorithms is demonstrated in a sequential Monte Carlo setting designed for sampling from distributions on spaces of decomposable graphs , where the junction-tree expander can be effectively employed as proposal kernel;
Edit intent: fluency
Original:   A direct application of our suggested algorithm is demonstrated in a sequential Monte Carlo setting designed for sampling from distributions on spaces of decomposable graphs , where the junction-tree expander can be effectively employed as proposal kernel;
Revised:  A direct application of our suggested algorithm is demonstrated in a sequential-Monte-Carlo setting designed for sampling from distributions on spaces of decomposable graphs , where the junction-tree expander can be effectively employed as proposal kernel;
Edit intent: clarity
Original:  see the companion paper Olsson et al. 2019 16%DIFDELCMD < ]%%% . A numerical study illustrates the utility of our approach by two examples: in the first one, how the junction-tree expander can be incorporated successfully into a particle Gibbs sampler for Bayesian structure learning in decomposable graphical models;
Revised:  see the companion paper Olsson et al. 2019 %DIFDELCMD < ]%%% . A numerical study illustrates the utility of our approach by two examples: in the first one, how the junction-tree expander can be incorporated successfully into a particle Gibbs sampler for Bayesian structure learning in decomposable graphical models;
Edit intent: coherence
Original:  see the companion paper Olsson et al. 2019 16%DIFDELCMD < ]%%% . A numerical study illustrates the utility of our approach by two examples: in the first one, how the junction-tree expander can be incorporated successfully into a particle Gibbs sampler for Bayesian structure learning in decomposable graphical models;
Revised:  see the companion paper Olsson et al. 2019 16%DIFDELCMD < ]%%% . Numerical studies illustrate the utility of our approach by two examples: in the first one, how the junction-tree expander can be incorporated successfully into a particle Gibbs sampler for Bayesian structure learning in decomposable graphical models;
Edit intent: fluency
Original: Recent advances in community detection reveal new insights into multiplex , time-dependent, and heterogeneously structured networks.
Revised: Advances in community detection reveal new insights into multiplex , time-dependent, and heterogeneously structured networks.
Edit intent: clarity
Original: Recent advances in community detection reveal new insights into multiplex , time-dependent, and heterogeneously structured networks.
Revised: Recent advances in community detection reveal new insights into multiplex and multilayer networks.
Edit intent: clarity
Original:  Less work, however, empirically investigates the relationship between membership in these communities and observable outcomes in social systems.
Revised:  Less work, however, investigates the relationship between membership in these communities and observable outcomes in social systems.
Edit intent: clarity
Original:  Less work, however, empirically investigates the relationship between membership in these communities and observable outcomes in social systems.
Revised:  Less work, however, empirically investigates the relationship between these communities and observable outcomes in social systems.
Edit intent: clarity
Original:  Less work, however, empirically investigates the relationship between membership in these communities and observable outcomes in social systems.
Revised:  Less work, however, empirically investigates the relationship between membership in these communities and outcomes in social systems.
Edit intent: clarity
Original:  We investigate this question in the domain of politics with an application to a crucial outcome of scholarly interest: the onset of violent conflict in the international system .
Revised:  We leverage these advances to shed light on the relationship between the cooperative mesostructure of the international system .
Edit intent: clarity
Original:  We achieve 5.5 microseconds of replication latency on lossy Ethernet, which is better than or comparable to specialized replication systems that use programmable switches, FPGAs, or RDMA.
Revised:  We achieve 5.5 microseconds of replication latency on lossy Ethernet, which is faster than or comparable to specialized replication systems that use programmable switches, FPGAs, or RDMA.
Edit intent: clarity
Original:  This is possible because individual group members  adjust their position and direction of movement in response to the position and motion of other group members.
Revised:  This is possible because individual group members repeatedly adjust their position and direction of movement in response to the position and motion of other group members.
Edit intent: clarity
Original:  Recent literature has focused on elucidating these 'interaction rules' that mediate group coordination for different animal species empirically from tracking data of real animal groups  .
Revised:  Recent literature has focused on investigating the interaction responses that mediate group coordination for different animal species empirically from tracking data of real animal groups .
Edit intent: clarity
Original:  Recent literature has focused on elucidating these 'interaction rules' that mediate group coordination for different animal species empirically from tracking data of real animal groups  .
Revised:  Recent literature has focused on elucidating these 'interaction rules' that mediate group coordination empirically from tracking data of real animal groups .
Edit intent: clarity
Original:  Recent literature has focused on elucidating these 'interaction rules' that mediate group coordination for different animal species empirically from tracking data of real animal groups  .
Revised:  Recent literature has focused on elucidating these 'interaction rules' that mediate group coordination for different animal species empirically from tracking data of real animal groups of various species .
Edit intent: clarity
Original:  Here, we adopt a complementary theoretical approach and we start by considering how the spatial organisation of a group would change in the complete absence of interactions.
Revised:  Here, we develop a complementary theoretical approach and we start by considering how the spatial organisation of a group would change in the complete absence of interactions.
Edit intent: clarity
Original:  Here, we adopt a complementary theoretical approach and we start by considering how the spatial organisation of a group would change in the complete absence of interactions.
Revised:  Here, we adopt a complementary theoretical approach in which we consider how the spatial organisation of a group would change in the complete absence of interactions.
Edit intent: coherence
Original:  In this condition, the group would disperse and its collective behaviour would be described in terms of a simple diffusion process .
Revised:  In this condition, the group would disperse in a way that can be characterised in terms of a simple diffusion process .
Edit intent: clarity
Original:  In this condition, the group would disperse and its collective behaviour would be described in terms of a simple diffusion process .
Revised:  In this condition, the group would disperse and its collective behaviour would be described in terms of Fick's diffusion equations .
Edit intent: clarity
Original:  We show that an individual-level response to neighbour densities in the form of a Weber's law (a response to gradient normalised over local density ) results in an 'anti-diffusion' term at the group level.
Revised:  We show that an individual-level response to neighbour densities in the form of a Weber's law (a response to gradient normalised over local densities ) results in an 'anti-diffusion' term at the group level.
Edit intent: fluency
Original:  Our study identifies a general form underlying all collective animal interaction rules and points to a link between collective interactions and the fundamental functioning of perceptual sytems.
Revised:  Our study identifies a general form underlying all collective animal interaction responses and points to a link between collective interactions and the fundamental functioning of perceptual sytems.
Edit intent: clarity
Original:  Our study identifies a general form underlying all collective animal interaction rules and points to a link between collective interactions and the fundamental functioning of perceptual sytems.
Revised:  Our study identifies a general form underlying all collective animal interaction rules and points to a link between collective behaviour and the fundamental functioning of perceptual sytems.
Edit intent: clarity
Original:  This is possible because individual group members repeatedly adjust their position and direction of movement in response to the position and motion of other group members.
Revised:  This is possible because individual group members repeatedly adjust their position and motion in response to the position and motion of other group members.
Edit intent: clarity
Original:  In this condition, the group would disperse in a way that can be  characterised in terms of Fick's diffusion equations.
Revised:  Without interactions, a group would disperse in a way that can be characterised in terms of Fick's diffusion equations.
Edit intent: clarity
Original:  In this condition, the group would disperse in a way that can be  characterised in terms of Fick's diffusion equations.
Revised:  In this condition, the group would disperse in a way that can be easily characterised in terms of Fick's diffusion equations.
Edit intent: clarity
Original:  We can hence address the inverse theoretical problem of finding the individual level interaction responses that are precisely required to counterbalance diffusion and  preserve group stability.
Revised:  We can hence address the inverse theoretical problem of finding the individual-level interaction responses that are precisely required to counterbalance diffusion and preserve group stability.
Edit intent: fluency
Original:  We can hence address the inverse theoretical problem of finding the individual level interaction responses that are precisely required to counterbalance diffusion and  preserve group stability.
Revised:  We can hence address the inverse theoretical problem of finding the individual level interaction responses that are required to counterbalance diffusion and preserve group stability.
Edit intent: clarity
Original:  We can hence address the inverse theoretical problem of finding the individual level interaction responses that are precisely required to counterbalance diffusion and  preserve group stability.
Revised:  We can hence address the inverse theoretical problem of finding the individual level interaction responses that are precisely required to counterbalance diffusion and to preserve group stability.
Edit intent: fluency
Original:  We show that an individual-level response to neighbour densities in the form of a Weber's law (a well-known law describing the functioning of sensory systems, which essentially corresponds to a response to gradients normalised over local densities ) results in an 'anti-diffusion' term at the group level.
Revised:  We show that an individual-level response to neighbour densities in the form of Weber's law (a well-known law describing the functioning of sensory systems, which essentially corresponds to a response to gradients normalised over local densities ) results in an 'anti-diffusion' term at the group level.
Edit intent: fluency
Original:  We show that an individual-level response to neighbour densities in the form of a Weber's law (a well-known law describing the functioning of sensory systems, which essentially corresponds to a response to gradients normalised over local densities ) results in an 'anti-diffusion' term at the group level.
Revised:  We show that an individual-level response to neighbour densities in the form of a Weber's law (a 'universal' law describing the functioning of sensory systems, which essentially corresponds to a response to gradients normalised over local densities ) results in an 'anti-diffusion' term at the group level.
Edit intent: clarity
Original:  We show that an individual-level response to neighbour densities in the form of a Weber's law (a well-known law describing the functioning of sensory systems, which essentially corresponds to a response to gradients normalised over local densities ) results in an 'anti-diffusion' term at the group level.
Revised:  We show that an individual-level response to neighbour densities in the form of a Weber's law (a well-known law describing the functioning of the sensory systems of animals of all species ) results in an 'anti-diffusion' term at the group level.
Edit intent: clarity
Original:  We further show that any non-homogeneous, spatial density distribution can be preserved over time if individual movement patterns have the form of a Weber's law response.
Revised:  We also show that any non-homogeneous, spatial density distribution can be preserved over time if individual movement patterns have the form of a Weber's law response.
Edit intent: clarity
Original:  Our study identifies a general form underlying all collective animal interaction responses and points to a link between collective behaviour and the fundamental functioning of perceptual sytems .
Revised:  Weber's law describes the fundamental functioning of perceptual sytems .
Edit intent: clarity
Original:  When a natural choice of the graph is not readily available from the datasets , it is thus desirable to infer or learn a graph topology from the data.
Revised:  When a natural choice of the graph is not readily available from the data sets , it is thus desirable to infer or learn a graph topology from the data.
Edit intent: clarity
Original:  We further emphasize the conceptual similarities and differences between classical and GSP graph inference methods  and highlight the potential advantage of the latter in a number of theoretical and practical scenarios.
Revised:  We further emphasize the conceptual similarities and differences between classical and GSP-based graph inference methods and highlight the potential advantage of the latter in a number of theoretical and practical scenarios.
Edit intent: clarity
Original:  We further emphasize the conceptual similarities and differences between classical and GSP graph inference methods  and highlight the potential advantage of the latter in a number of theoretical and practical scenarios.
Revised:  We further emphasize the conceptual similarities and differences between classical and GSP graph inference methods , and highlight the potential advantage of the latter in a number of theoretical and practical scenarios.
Edit intent: fluency
Original:  The transition phase of a dynamic Navier-Stokes solution to the periodic state can be excessively long and it depends on  the domain size and on problem parameters like the viscosity.
Revised:  The transition phase of a dynamic Navier-Stokes solution to the periodic state can be excessively long and it depends on parameters like the domain size and on problem parameters like the viscosity.
Edit intent: fluency
Original:  The transition phase of a dynamic Navier-Stokes solution to the periodic state can be excessively long and it depends on  the domain size and on problem parameters like the viscosity.
Revised:  The transition phase of a dynamic Navier-Stokes solution to the periodic state can be excessively long and it depends on the domain size and the viscosity.
Edit intent: clarity
Original:  Several methods for acceleration exist.
Revised:  Several methods for an accelerated identification of the correct initial data that will yield the periodic state exist.
Edit intent: clarity
Original:  They are either based on a space-time framework for directly computing the periodic state , on optimization schemes or shooting methods for quickly finding the correct initial data that yields the periodic solution.
Revised:  They are mostly based on space-time framework for directly computing the periodic state , on optimization schemes or shooting methods for quickly finding the correct initial data that yields the periodic solution.
Edit intent: clarity
Original:  They are either based on a space-time framework for directly computing the periodic state , on optimization schemes or shooting methods for quickly finding the correct initial data that yields the periodic solution.
Revised:  They are either based on a space-time frameworks for directly computing the periodic state , on optimization schemes or shooting methods for quickly finding the correct initial data that yields the periodic solution.
Edit intent: fluency
Original:  They are either based on a space-time framework for directly computing the periodic state , on optimization schemes or shooting methods for quickly finding the correct initial data that yields the periodic solution.
Revised:  They are either based on a space-time framework for directly computing the periodic state or on optimization schemes or shooting methods for quickly finding the correct initial data that yields the periodic solution.
Edit intent: fluency
Original: Grid cells in the medial entorhinal cortex ( mEC ) respond when an animal occupies a periodic lattice of "grid fields" in the environment.
Revised: Grid cells in the medial entorhinal cortex ( MEC ) respond when an animal occupies a periodic lattice of "grid fields" in the environment.
Edit intent: fluency
Original:  The grids are organized in modules with spatial periods  clustered around discrete values separated by constant ratios reported in the range 1.3-1.8 . We propose a mechanism for dynamical self-organization in the mEC that can produce this modular structure  .
Revised:  The grids are organized in modules with spatial periods clustered around discrete values separated by ratios in the range 1.3-1.8 . We propose a mechanism for dynamical self-organization in the mEC that can produce this modular structure .
Edit intent: clarity