wanyu/IteraTeR_v2 huggingface dataset:
Original:  Our simulations show that Simulated Annealing can outperform QAOA for BLLS at a circuit depth of p\leq3 for the probability of sampling the ground state.
Revised:  Our simulations show that Simulated Annealing can outperform QAOA for BLLS at a QAOA depth of p\leq3 for the probability of sampling the ground state.
Edit intent: clarity
Original:  Finally, we point out some of the challenges involved in current-day experimental implementations of this technique on a cloud-based quantum computer .
Revised:  Finally, we point out some of the challenges involved in current-day experimental implementations of this technique on cloud-based quantum computer .
Edit intent: fluency
Original:  Finally, we point out some of the challenges involved in current-day experimental implementations of this technique on a cloud-based quantum computer .
Revised:  Finally, we point out some of the challenges involved in current-day experimental implementations of this technique on a cloud-based quantum computers .
Edit intent: fluency
Original:  Inspired by the structural balance theory, in this article, we innovatively propose a non-backtracking operator for signed networks .
Revised:  In this article, we innovatively propose a non-backtracking operator for signed networks .
Edit intent: coherence
Original:  Inspired by the structural balance theory, in this article, we innovatively propose a non-backtracking operator for signed networks .
Revised:  Inspired by the structural balance theory, in this article, we innovatively propose a non-backtracking matrix for signed networks .
Edit intent: clarity
Original:  Besides, we theoretically derive a detectability threshold and prove the feasibility of the non-backtracking operator in community detection.
Revised:  Besides, we theoretically derive a detectability threshold and prove the feasibility in community detection.
Edit intent: clarity
Original: Community detection or clustering is crucial for understanding the structure of complex systems.
Revised: Community detection or clustering is a crucial task for understanding the structure of complex systems.
Edit intent: clarity
Original:  In some networks, nodes are allowed to be linked by either 'positive' or 'negative' edges.
Revised:  In some networks, nodes are permitted to be linked by either 'positive' or 'negative' edges.
Edit intent: fluency
Original:  Discovering communities in signed networks is more challenging  .
Revised:  Discovering communities in signed networks is more challenging than that in unsigned networks .
Edit intent: clarity
Original:  In this article , we innovatively propose a non-backtracking matrix for signed networks, and theoretically derive a detectability threshold and prove the feasibility in community detection.
Revised:  In this study , we innovatively propose a non-backtracking matrix for signed networks, and theoretically derive a detectability threshold and prove the feasibility in community detection.
Edit intent: clarity
Original:  In this article , we innovatively propose a non-backtracking matrix for signed networks, and theoretically derive a detectability threshold and prove the feasibility in community detection.
Revised:  In this article , we innovatively develop a non-backtracking matrix for signed networks, and theoretically derive a detectability threshold and prove the feasibility in community detection.
Edit intent: clarity
Original:  In this article , we innovatively propose a non-backtracking matrix for signed networks, and theoretically derive a detectability threshold and prove the feasibility in community detection.
Revised:  In this article , we innovatively propose a non-backtracking matrix of signed networks, and theoretically derive a detectability threshold and prove the feasibility in community detection.
Edit intent: fluency
Original:  In this article , we innovatively propose a non-backtracking matrix for signed networks, and theoretically derive a detectability threshold and prove the feasibility in community detection.
Revised:  In this article , we innovatively propose a non-backtracking matrix for signed networks, theoretically derive a detectability threshold and prove the feasibility in community detection.
Edit intent: fluency
Original:  In this article , we innovatively propose a non-backtracking matrix for signed networks, and theoretically derive a detectability threshold and prove the feasibility in community detection.
Revised:  In this article , we innovatively propose a non-backtracking matrix for signed networks, and theoretically derive a detectability threshold for this matrix, and demonstrate the feasibility of using the matrix for community detection.
Edit intent: clarity
Original:  Furthermore, we improve the operator by considering the balanced paths in the network ( denoted as balanced non-backtracking operator ).
Revised:  We further improve the developed matrix by considering the balanced paths in the network ( denoted as balanced non-backtracking operator ).
Edit intent: clarity
Original:  Furthermore, we improve the operator by considering the balanced paths in the network ( denoted as balanced non-backtracking operator ).
Revised:  Furthermore, we improve the operator by considering the balanced paths in the network ( referred to as a balanced non-backtracking operator ).
Edit intent: coherence
Original:  Furthermore, we improve the operator by considering the balanced paths in the network ( denoted as balanced non-backtracking operator ).
Revised:  Furthermore, we improve the operator by considering the balanced paths in the network ( denoted as balanced non-backtracking matrix ).
Edit intent: clarity
Original:  Simulation results demonstrate that the balanced non-backtracking matrix-based approach significantly outperforms the adjacency matrix-based and the signed non-backtracking matrix-based algorithm.
Revised:  Simulation results demonstrate that the algorithm based on the balanced nonbacktracking matrix significantly outperforms those based on the adjacency matrix and the signed non-backtracking matrix-based algorithm.
Edit intent: clarity
Original:  It shows great potential to detect communities with or without overlap.
Revised:  It shows great potential for detecting communities with or without overlap.
Edit intent: fluency
Original: We discuss a stochastic model to assess cumulative excess deaths during Covid-19-like epidemics for various non-pharmaceutic interventions.
Revised: We discuss a stochastic model to assess the cumulative number of deaths during hypothetical Covid-19-like epidemics for various non-pharmaceutic interventions.
Edit intent: clarity
Original:  Epidemic is modelled as a discrete time stochastic process on random geometric networks.
Revised:  Epidemic spreading is modeled as a discrete-time stochastic process on random geometric networks.
Edit intent: clarity
Original:  In the simulations we assume that the basic reproduction number is R_0= 2.5 and the infectious period lasts ca. ten days.
Revised:  In the simulations we assume that the basic reproduction number is 2.5 and the infectious period lasts ca. ten days.
Edit intent: coherence
Original:  In the simulations we assume that the basic reproduction number is R_0= 2.5 and the infectious period lasts ca. ten days.
Revised:  In the simulations we assume that the basic reproduction number is R_0= 2.5 and the infectious period lasts approximately ten days.
Edit intent: clarity
Original:  For other parameters , like mortality rate or the number of respiratory ventilators per million of inhabitants, we take values typical for developed countries.
Revised:  For other parameters , like mortality rates or the number of respiratory ventilators per million of inhabitants, we take values typical for developed countries.
Edit intent: fluency
Original:  The results of the simulations show that strategies that slow down the spread of epidemic too much are inefficient in reducing the cumulative excess of deaths .
Revised:  The results of the simulations show that strategies that slow the development of an epidemic too much are inefficient in reducing the cumulative excess of deaths .
Edit intent: clarity
Original:  A hybrid strategy in which lockdown is in place for some time and is then completely released is inefficient as well .
Revised:  A hybrid strategy in which lockdown is in place for some time and is then completely released , is inefficient .
Edit intent: clarity
Original:  Online platforms that sex workers use to advertise services have become an increasingly important tool in studying a market that is largely hidden.
Revised:  Online platforms that sex workers use to advertise services have become an increasingly important means of studying a market that is largely hidden.
Edit intent: clarity
Original:  While the size of these influences vary across genders, nationality, age , and services provided are shown to be primary drivers of rates and popularity in sex work.
Revised:  While the size of these influences varies across genders, nationality, age , and services provided are shown to be primary drivers of rates and popularity in sex work.
Edit intent: fluency
Original:  While the size of these influences vary across genders, nationality, age , and services provided are shown to be primary drivers of rates and popularity in sex work.
Revised:  While the size of these influences vary across genders, nationality, age and the services provided are shown to be primary drivers of rates and popularity in sex work.
Edit intent: fluency
Original: Publicly available electrical generation and interconnector data is combined to create a half-hourly dataset for Great Britains electrical demand .
Revised: A method is presented to combine publicly available electrical generation and interconnector data is combined to create a half-hourly dataset for Great Britains electrical demand .
Edit intent: clarity
Original: Publicly available electrical generation and interconnector data is combined to create a half-hourly dataset for Great Britains electrical demand .
Revised: Publicly available electrical generation and interconnector data to create a half-hourly dataset for Great Britains electrical demand .
Edit intent: clarity
Original:  The method uses Elexon data for power plants connected at the transmission level , monitored as part of the balancing mechanism, and combines these with the estimates for embedded generation for solar and wind generation from the system operator National Grid.
Revised:  The method uses Elexon data for generation plants connected at the transmission level , monitored as part of the balancing mechanism, and combines these with the estimates for embedded generation for solar and wind generation from the system operator National Grid.
Edit intent: clarity
Original:  The method uses Elexon data for power plants connected at the transmission level , monitored as part of the balancing mechanism, and combines these with the estimates for embedded generation for solar and wind generation from the system operator National Grid.
Revised:  The method uses Elexon data for power plants connected at the transmission level that are monitored as part of the balancing mechanism, and combines these with the estimates for embedded generation for solar and wind generation from the system operator National Grid.
Edit intent: clarity
Original:  The method uses Elexon data for power plants connected at the transmission level , monitored as part of the balancing mechanism, and combines these with the estimates for embedded generation for solar and wind generation from the system operator National Grid.
Revised:  The method uses Elexon data for power plants connected at the transmission level , monitored as part of the balancing mechanism, and combines these with estimates for embedded generation for solar and wind generation from the system operator National Grid.
Edit intent: fluency
Original:  The method uses Elexon data for power plants connected at the transmission level , monitored as part of the balancing mechanism, and combines these with the estimates for embedded generation for solar and wind generation from the system operator National Grid.
Revised:  The method uses Elexon data for power plants connected at the transmission level , monitored as part of the balancing mechanism, and combines these with the estimates for embedded /distributed solar and wind generation from the system operator National Grid.
Edit intent: clarity
Original: A method is presented to combine publicly available electrical generation and interconnector data to create a timeseries dataset that approximates Great Britains half-hourly electrical demandfor its public distribution system.
Revised: Here we present a method to combine half-hourly publicly available electrical generation and interconnector data to create a timeseries dataset that approximates Great Britains half-hourly electrical demandfor its public distribution system.
Edit intent: clarity
Original: A method is presented to combine publicly available electrical generation and interconnector data to create a timeseries dataset that approximates Great Britains half-hourly electrical demandfor its public distribution system.
Revised: A method is presented to combine publicly available electrical generation and interconnector data to create a timeseries that approximates Great Britains half-hourly electrical demandfor its public distribution system.
Edit intent: clarity
Original:  The data are presented in a raw as well as a visually checked and cleaned form and have been parsed to provide both coordinated universal time (UTC) and localtime values in ISO 8601 compatible format, making the data significantly more interoperable with other data , and more useable by a wider group of researchers and stakeholders .
Revised:  The data are presented in a raw as well as a visually checked and cleaned form and have been parsed to provide both coordinated universal time (UTC) and localtime values in ISO 8601 compatible datetimes to increase interoperability with other data , and more useable by a wider group of researchers and stakeholders .
Edit intent: clarity
Original:  The data are presented in a raw as well as a visually checked and cleaned form and have been parsed to provide both coordinated universal time (UTC) and localtime values in ISO 8601 compatible format, making the data significantly more interoperable with other data , and more useable by a wider group of researchers and stakeholders .
Revised:  The data are presented in a raw as well as a visually checked and cleaned form and have been parsed to provide both coordinated universal time (UTC) and localtime values in ISO 8601 compatible format, making the data significantly more interoperable with other data . The published data is therefore more useable by a wider group of researchers and stakeholders .
Edit intent: coherence
Original: Here we present a method to combine half-hourly publicly available electrical generation and interconnector data to create a timeseries that approximates Great Britains electrical demand.
Revised: Here we present a method to combine half-hourly publicly available electrical generation and interconnector operational data for Great Britain to create a timeseries that approximates Great Britains electrical demand.
Edit intent: clarity
Original: Here we present a method to combine half-hourly publicly available electrical generation and interconnector data to create a timeseries that approximates Great Britains electrical demand.
Revised: Here we present a method to combine half-hourly publicly available electrical generation and interconnector data to create a timeseries that approximates its electrical demand.
Edit intent: fluency
Original:  The published data is therefore more useable by a wider group of researchers and stakeholders interested in an example of the rapid decarbonisation of a countries electrical system .
Revised:  The published data is therefore more useable by a wider group of researchers and stakeholders interested in an example of rapid decarbonisation of a countries electrical system .
Edit intent: fluency
Original: Deep learning has significantly revolutionized the design of numerical algorithms for solving high-dimensional partial differential equations (PDEs) .
Revised: The problem of solving partial differential equations (PDEs) .
Edit intent: clarity
Original:  A global minimizer corresponds to a deep neural network that solves the given PDE.
Revised:  A global minimizer corresponds to a neural network that solves the given PDE.
Edit intent: clarity
Original: The Hylland-Zeckhauser (HZ) rule is a well-known rule for probabilistic assignment of items.
Revised: The Hylland-Zeckhauser (HZ) rule is a well-known rule for random assignment of items.
Edit intent: clarity
Original:  We also clarify which results change when moving from 1-0 binary utilities to the more general bi-valued  utilities.
Revised:  We clarify which results change when moving from 1-0 binary utilities to the more general bi-valued utilities.
Edit intent: clarity
Original: In this paper, we present a reinforcement learning approach to designing a control policy for a "leader '' agent that herds a swarm of "follower '' agents, via repulsive interactions, as quickly as possible to a target probability distribution over a strongly connected graph.
Revised: In this paper, we present a reinforcement learning approach to designing a control policy for a "leader " agent that herds a swarm of "follower '' agents, via repulsive interactions, as quickly as possible to a target probability distribution over a strongly connected graph.
Edit intent: fluency
Original: In this paper, we present a reinforcement learning approach to designing a control policy for a "leader '' agent that herds a swarm of "follower '' agents, via repulsive interactions, as quickly as possible to a target probability distribution over a strongly connected graph.
Revised: In this paper, we present a reinforcement learning approach to designing a control policy for a "leader '' agent that herds a swarm of "follower " agents, via repulsive interactions, as quickly as possible to a target probability distribution over a strongly connected graph.
Edit intent: fluency
Original: For a given \varepsilon > 0, we say that a graph G is \epsilon -flexibly k-choosable if the following holds: for any assignment L of  lists of size k on V(G), if a preferred color  is requested at any set R of vertices, then at least \epsilon |R| of these requests may be satisfied by some L-coloring.
Revised: For a given \varepsilon > 0, we say that a graph G is \varepsilon -flexibly k-choosable if the following holds: for any assignment L of lists of size k on V(G), if a preferred color is requested at any set R of vertices, then at least \epsilon |R| of these requests may be satisfied by some L-coloring.
Edit intent: fluency
Original: For a given \varepsilon > 0, we say that a graph G is \epsilon -flexibly k-choosable if the following holds: for any assignment L of  lists of size k on V(G), if a preferred color  is requested at any set R of vertices, then at least \epsilon |R| of these requests may be satisfied by some L-coloring.
Revised: For a given \varepsilon > 0, we say that a graph G is \epsilon -flexibly k-choosable if the following holds: for any assignment L of color lists of size k on V(G), if a preferred color is requested at any set R of vertices, then at least \epsilon |R| of these requests may be satisfied by some L-coloring.
Edit intent: fluency
Original: For a given \varepsilon > 0, we say that a graph G is \epsilon -flexibly k-choosable if the following holds: for any assignment L of  lists of size k on V(G), if a preferred color  is requested at any set R of vertices, then at least \epsilon |R| of these requests may be satisfied by some L-coloring.
Revised: For a given \varepsilon > 0, we say that a graph G is \epsilon -flexibly k-choosable if the following holds: for any assignment L of lists of size k on V(G), if a preferred color from a list is requested at any set R of vertices, then at least \epsilon |R| of these requests may be satisfied by some L-coloring.
Edit intent: clarity
Original: For a given \varepsilon > 0, we say that a graph G is \epsilon -flexibly k-choosable if the following holds: for any assignment L of  lists of size k on V(G), if a preferred color  is requested at any set R of vertices, then at least \epsilon |R| of these requests may be satisfied by some L-coloring.
Revised: For a given \varepsilon > 0, we say that a graph G is \epsilon -flexibly k-choosable if the following holds: for any assignment L of lists of size k on V(G), if a preferred color is requested at any set R of vertices, then at least \varepsilon |R| of these requests may be satisfied by some L-coloring.
Edit intent: fluency
Original: For a given \varepsilon > 0, we say that a graph G is \epsilon -flexibly k-choosable if the following holds: for any assignment L of  lists of size k on V(G), if a preferred color  is requested at any set R of vertices, then at least \epsilon |R| of these requests may be satisfied by some L-coloring.
Revised: For a given \varepsilon > 0, we say that a graph G is \epsilon -flexibly k-choosable if the following holds: for any assignment L of lists of size k on V(G), if a preferred color is requested at any set R of vertices, then at least \epsilon |R| of these requests are satisfied by some L-coloring.
Edit intent: clarity
Original:  We consider flexible list colorings in several graph classes with certain special degeneracy conditions.
Revised:  We consider the question of flexible choosability in several graph classes with certain special degeneracy conditions.
Edit intent: clarity
Original:  We consider flexible list colorings in several graph classes with certain special degeneracy conditions.
Revised:  We consider flexible list colorings in several graph classes with certain degeneracy conditions.
Edit intent: clarity
Original:  We characterize the graphs of maximum degree \Delta that are \epsilon -flexibly \Delta-choosable for some \epsilon = \epsilon (\Delta) > 0, which answers a question of Dvo\v{r}\'ak, Norin, and Postle [List coloring with requests, JGT 2019].  is \frac{1}{6\Delta}-flexibly \Delta-choosable.
Revised:  We characterize the graphs of maximum degree \Delta that are \varepsilon -flexibly \Delta-choosable for some \epsilon = \epsilon (\Delta) > 0, which answers a question of Dvo\v{r}\'ak, Norin, and Postle [List coloring with requests, JGT 2019]. is \frac{1}{6\Delta}-flexibly \Delta-choosable.
Edit intent: fluency
Original:  We characterize the graphs of maximum degree \Delta that are \epsilon -flexibly \Delta-choosable for some \epsilon = \epsilon (\Delta) > 0, which answers a question of Dvo\v{r}\'ak, Norin, and Postle [List coloring with requests, JGT 2019].  is \frac{1}{6\Delta}-flexibly \Delta-choosable.
Revised:  We characterize the graphs of maximum degree \Delta that are \epsilon -flexibly \Delta-choosable for some \varepsilon = \epsilon (\Delta) > 0, which answers a question of Dvo\v{r}\'ak, Norin, and Postle [List coloring with requests, JGT 2019]. is \frac{1}{6\Delta}-flexibly \Delta-choosable.
Edit intent: fluency
Original:  We characterize the graphs of maximum degree \Delta that are \epsilon -flexibly \Delta-choosable for some \epsilon = \epsilon (\Delta) > 0, which answers a question of Dvo\v{r}\'ak, Norin, and Postle [List coloring with requests, JGT 2019].  is \frac{1}{6\Delta}-flexibly \Delta-choosable.
Revised:  We characterize the graphs of maximum degree \Delta that are \epsilon -flexibly \Delta-choosable for some \epsilon = \varepsilon (\Delta) > 0, which answers a question of Dvo\v{r}\'ak, Norin, and Postle [List coloring with requests, JGT 2019]. is \frac{1}{6\Delta}-flexibly \Delta-choosable.
Edit intent: fluency
Original:  } We also show that graphs of treewidth 2 are \frac{1}{3}-flexibly 3-choosable, answering a question of I. Choi et al.
Revised:  } We also show that graphs of treewidth 2 are \frac{1}{3}-flexibly 3-choosable, answering a question of Choi et al.
Edit intent: clarity