wanyu/IteraTeR_v2 huggingface dataset:
Original:  The combined framework offers a fundamental alternative to existing approaches to investigating functional connectivity in the brain, from voxel- or seed-pair wise characterizations of functional association, towards a full  multivariate characterization of spatial connectopies .
Revised:  The combined framework offers a fundamental alternative to existing approaches to investigating functional connectivity in the brain, from voxel- or seed-pair wise characterizations of functional association, towards a full , multivariate characterization of spatial connectopies .
Edit intent: fluency
Original:  The combined framework offers a fundamental alternative to existing approaches to investigating functional connectivity in the brain, from voxel- or seed-pair wise characterizations of functional association, towards a full  multivariate characterization of spatial connectopies .
Revised:  The combined framework offers a fundamental alternative to existing approaches to investigating functional connectivity in the brain, from voxel- or seed-pair wise characterizations of functional association, towards a full multivariate characterization of spatial topography .
Edit intent: clarity
Original:  This problem is a natural restriction of the maximum common subgraph problem, which is NP-hard {\sf   in general graphs.
Revised:  This problem is a natural restriction of the maximum common subgraph problem, which is {\sf in general graphs.
Edit intent: clarity
Original:  Combining a polynomial-delay algorithm for the enumeration of all maximum common subtree isomorphisms with central ideas of our new algorithm leads to an improvement of its running time from O (n^6+Tn^2) to O (n^3+Tn\Delta), where n is the order of the larger tree, T is the number of different solutions, and \Delta is the minimum of the maximum node degrees of the input trees.
Revised:  Combining a polynomial-delay algorithm for the enumeration of all maximum common subtree isomorphisms with central ideas of our new algorithm leads to an improvement of its running time from O (n^6+Tn^2) to O (n^3+Tn\Delta), where n is the order of the larger tree, T is the number of different solutions, and \Delta is the minimum of the maximum degrees of the input trees.
Edit intent: clarity
Original:  In this paper we show that the previously introduced operators for obtaining triconcepts and maximal connected and complete sets ( MCCS ) are not always consistent and provide the reader with a definition of valid closure operator and associated set system  .
Revised:  In this paper we show that the previously introduced operators for obtaining triconcepts and maximal connected and complete sets ( MCCSs ) are not always consistent and provide the reader with a definition of valid closure operator and associated set system .
Edit intent: fluency
Original:  Given an arbitrary convex shape C, a constrained Delaunay graph is constructed by adding an edge between two vertices p and q if and only if there exists a homothet of C with p and q on its boundary that does not contain any other vertices visible to p and  q. We show that, regardless of the convex shape C used to construct the constrained Delaunay graph, there exists a constant t (that depends on  C) such that it is a plane t-spanner  .
Revised:  Given an arbitrary convex shape C, a constrained Delaunay graph is constructed by adding an edge between two vertices p and q if and only if there exists a homothet of C with p and q on its boundary that does not contain any other vertices visible to p and ~ q. We show that, regardless of the convex shape C used to construct the constrained Delaunay graph, there exists a constant t (that depends on C) such that it is a plane t-spanner .
Edit intent: clarity
Original:  Given an arbitrary convex shape C, a constrained Delaunay graph is constructed by adding an edge between two vertices p and q if and only if there exists a homothet of C with p and q on its boundary that does not contain any other vertices visible to p and ~ q. We show that, regardless of the convex shape C used to construct the constrained Delaunay graph, there exists a constant t (that depends on ~ C) such that it is a plane t-spanner of the visibility graph.
Revised:  Given an arbitrary convex shape C, a constrained Delaunay graph is constructed by adding an edge between two vertices p and q if and only if there exists a homothet of C with p and q on its boundary that does not contain any other vertices visible to p and q. We show that, regardless of the convex shape C used to construct the constrained Delaunay graph, there exists a constant t (that depends on ~ C) such that it is a plane t-spanner of the visibility graph.
Edit intent: coherence
Original:  Given an arbitrary convex shape C, a constrained Delaunay graph is constructed by adding an edge between two vertices p and q if and only if there exists a homothet of C with p and q on its boundary that does not contain any other vertices visible to p and ~ q. We show that, regardless of the convex shape C used to construct the constrained Delaunay graph, there exists a constant t (that depends on ~ C) such that it is a plane t-spanner of the visibility graph.
Revised:  Given an arbitrary convex shape C, a constrained Delaunay graph is constructed by adding an edge between two vertices p and q if and only if there exists a homothet of C with p and q on its boundary that does not contain any other vertices visible to p and ~ q. We show that, regardless of the convex shape C used to construct the constrained Delaunay graph, there exists a constant t (that depends on C) such that it is a plane t-spanner of the visibility graph.
Edit intent: fluency
Original: The major structural ingredients of the brain and neural connectomes have been identified in recent years.
Revised: The large-scale structural ingredients of the brain and neural connectomes have been identified in recent years.
Edit intent: clarity
Original:  These are (i) the arrangement of the networks into modules and (ii) the presence of highly connected regions (hubs) forming so-called rich-clubs.
Revised:  These are (i) the arrangement of the networks into modules and the presence of highly connected regions (hubs) forming so-called rich-clubs.
Edit intent: fluency
Original:  These are (i) the arrangement of the networks into modules and (ii) the presence of highly connected regions (hubs) forming so-called rich-clubs.
Revised:  These are (i) the arrangement of the networks into modules and (ii) the presence of highly connected regions (hubs) forming rich-clubs.
Edit intent: clarity
Original:  It has been speculated that the combination of these features allows the brain to segregate and integrate information but a de- tailed investigation of their functional implications is missing.
Edit intent: coherence
Original:  Here, we examine how these network properties shape the collective dynamics of the brain.
Revised:  Here, we examine how modules and hubs shape the collective dynamics of the brain.
Edit intent: clarity
Original:  We find that both ingredients are crucial for the brain to host complex dynamical behaviour . Comparing the connectomes of C. elegans, cats, macaques and humans to surrogate networks in which one of the two features is destroyed, the functional complexity of the perturbed networks is always decreased.
Revised:  We find that both ingredients lead to the emergence of complex dynamics . Comparing the connectomes of C. elegans, cats, macaques and humans to surrogate networks in which one of the two features is destroyed, the functional complexity of the perturbed networks is always decreased.
Edit intent: clarity
Original:  Moreover, a comparison between simulated and empirically obtained resting-state functional connectivity indicates that the human brain, at rest, is in a dynamical state that reflects the largest complexity the anatomical connectome is able to host.
Revised:  Moreover, a comparison between simulated and empirically obtained resting-state functional connectivity indicates that the human brain, at rest, lies in a dynamical state that reflects the largest complexity the anatomical connectome is able to host.
Edit intent: clarity
Original:  Our model hosts more complex dynamics than the hierarchical network models previously defined and widely used as benchmarks.
Revised:  Our model hosts more complex dynamics than other hierarchical models widely used as benchmarks.
Edit intent: clarity
Original: Incompleteness theorems of G\"odel , Turing, Chaitin  and Algorithmic Information Theory have profound epistemological implications.
Revised: Incompleteness theorems of Godel , Turing, Chaitin and Algorithmic Information Theory have profound epistemological implications.
Edit intent: fluency
Original: Incompleteness theorems of G\"odel , Turing, Chaitin  and Algorithmic Information Theory have profound epistemological implications.
Revised: Incompleteness theorems of G\"odel , Turing, Chaitin , and Algorithmic Information Theory have profound epistemological implications.
Edit intent: fluency
Original:  This is an effort to convey these thoughts , some of which are original, in a somewhat entertaining manner.
Revised:  This is an effort to convey these thoughts and results in a somewhat entertaining manner.
Edit intent: clarity
Original: Learning non-linear functions can be hard when the magnitude of the target function is unknown beforehand, as most learning algorithms are not scale invariant .
Revised: Most learning algorithms are not scale invariant .
Edit intent: coherence
Original: Learning non-linear functions can be hard when the magnitude of the target function is unknown beforehand, as most learning algorithms are not scale invariant .
Revised: Learning non-linear functions can be hard when the magnitude of the target function is unknown beforehand, as most learning algorithms are not invariant to the scale of the function that is being approximated .
Edit intent: clarity
Original:  We propose an algorithm to adaptively normalize these targets .
Revised:  We propose to adaptively normalize these targets .
Edit intent: clarity
Original:  We propose an algorithm to adaptively normalize these targets .
Revised:  We propose an algorithm to adaptively normalize the targets used in learning .
Edit intent: clarity
Original:  Using our adaptive normalization we can remove this  heuristic without diminishing overall performance , and even improve performance on some games, such as Ms. Pac-Man and Centipede, on which previous methods did not perform well .
Revised:  Using our adaptive normalization we can remove this heuristic without diminishing overall performance .
Edit intent: coherence
Original: The Quantum Query Model is a framework that allow us to express most known quantum algorithms.
Revised: The Quantum Query Model is a framework that allows us to express most known quantum algorithms.
Edit intent: fluency
Original:  If we take the same measurement step on the Quantum Query Model and on the Block Set Formulation  , then we prove that both formulations give the same Gram matrix of output states, although the Block Set Formulation allows a much more explicit form.
Revised:  If we define the measurement step for the Block Set Formulation , then we prove that both formulations give the same Gram matrix of output states, although the Block Set Formulation allows a much more explicit form.
Edit intent: clarity
Original:  Therefore, the Block Set reformulation of the Quantum Query Model has advantages for the design of exact quantum algorithms .
Revised:  Therefore, the Block Set reformulation of the Quantum Query Model gives us an alternative interpretation on how quantum algorithms works .
Edit intent: clarity
Original:  Finally, we test these advantages of Block Sets by applying our approach to the construction of quantum exact algorithms.
Revised:  Finally, we apply our approach to the construction of quantum exact algorithms.
Edit intent: coherence
Original:  However, to overcome the high isotropic pathloss experienced at these frequencies, high directionality will be required at both the base station and the mobile user equipment to establish sufficient link budget in wide area net- works .
Revised:  However, to overcome the high isotropic pathloss experienced at these frequencies, high directionality will be required at both the base station and the mobile user equipment to establish sufficient link budget in wide area networks .
Edit intent: clarity
Original:  A coverage and delay analysis is performed to compare various techniques including exhaustive and iterative search, and Context-Information based algorithms.
Revised:  A coverage and delay analysis is performed to compare various techniques including exhaustive and iterative search, and Context Information based algorithms.
Edit intent: fluency
Original:  We prove an order-optimal regret bound w.r.t. the optimal memoryless policy and efficient scaling with respect to the dimensionality of observation and action spaces.
Revised:  We prove an order-optimal regret bound with respect to the optimal memoryless policy and efficient scaling with respect to the dimensionality of observation and action spaces.
Edit intent: coherence
Original: In this paper we study the pricing and hedging problem of a portfolio of life insurance products under the benchmark approach, where the reference market is modelled as driven by a state variable following a polynomial preserving diffusion on a compact state space.
Revised: In this paper we study the pricing and hedging problem of a portfolio of life insurance products under the benchmark approach, where the reference market is modelled as driven by a state variable following a polynomial diffusion on a compact state space.
Edit intent: clarity
Original: Recently, there has been immense interest in using unmanned aerial vehicles (UAVs) for civilian operations such as package delivery, aerial surveillance, and disaster response .
Revised: Recently, there has been immense interest in using unmanned aerial vehicles (UAVs) for civilian operations .
Edit intent: clarity
Original:  As a result, UAV traffic management systems are needed to support potentially thousands of UAVs flying simultaneously in the air space, in order to ensure their liveness and safety requirements are met . Currently, the analysis of large multi-agent systems cannot tractably provide these guarantees if the agents' set of maneuvers are unrestricted.
Revised:  As a result, unmanned aerial systems traffic management is needed to ensure the safety and liveness of potentially thousands of UAVs flying simultaneously in the air space, in order to ensure their liveness and safety requirements are met . Currently, the analysis of large multi-agent systems cannot tractably provide these guarantees if the agents' set of maneuvers are unrestricted.
Edit intent: clarity
Original:  As a result, UAV traffic management systems are needed to support potentially thousands of UAVs flying simultaneously in the air space, in order to ensure their liveness and safety requirements are met . Currently, the analysis of large multi-agent systems cannot tractably provide these guarantees if the agents' set of maneuvers are unrestricted.
Revised:  As a result, UAV traffic management systems are needed to support potentially thousands of UAVs flying simultaneously . Currently, the analysis of large multi-agent systems cannot tractably provide these guarantees if the agents' set of maneuvers are unrestricted.
Edit intent: coherence
Original:  As a result, UAV traffic management systems are needed to support potentially thousands of UAVs flying simultaneously in the air space, in order to ensure their liveness and safety requirements are met . Currently, the analysis of large multi-agent systems cannot tractably provide these guarantees if the agents' set of maneuvers are unrestricted.
Revised:  As a result, UAV traffic management systems are needed to support potentially thousands of UAVs flying simultaneously in the air space, in order to ensure their liveness and safety requirements are met . Currently, the analysis of large multi-agent systems cannot tractably provide safety and liveness guarantees if the agents' set of maneuvers are unrestricted.
Edit intent: clarity
Original:  As a result, UAV traffic management systems are needed to support potentially thousands of UAVs flying simultaneously in the air space, in order to ensure their liveness and safety requirements are met . Currently, the analysis of large multi-agent systems cannot tractably provide these guarantees if the agents' set of maneuvers are unrestricted.
Revised:  As a result, UAV traffic management systems are needed to support potentially thousands of UAVs flying simultaneously in the air space, in order to ensure their liveness and safety requirements are met . Currently, the analysis of large multi-agent systems cannot tractably provide these guarantees if the agents' set of maneuvers is unrestricted.
Edit intent: fluency
Original:  In this paper, we propose to have platoons of UAVs flying on air highways in order to impose the air space structure that allows for tractable analysis and intuitive monitoring .
Revised:  In this paper, platoons of UAVs flying on air highways in order to impose the air space structure that allows for tractable analysis and intuitive monitoring .
Edit intent: clarity
Original:  In this paper, we propose to have platoons of UAVs flying on air highways in order to impose the air space structure that allows for tractable analysis and intuitive monitoring .
Revised:  In this paper, we propose to have platoons of UAVs flying on air highways is proposed to impose an airspace structure that allows for tractable analysis and intuitive monitoring .
Edit intent: clarity
Original:  In this paper, we propose to have platoons of UAVs flying on air highways in order to impose the air space structure that allows for tractable analysis and intuitive monitoring .
Revised:  In this paper, we propose to have platoons of UAVs flying on air highways in order to impose the air space structure that allows for tractable analysis .
Edit intent: clarity
Original:  For the air highway placement problem, we use the flexible and efficient fast marching method to solve the Eikonal equation, which produces a sequence of air highways that minimizes the cost of flying from an origin to any destination.
Revised:  For the air highway placement problem, the fast marching method to solve the Eikonal equation, which produces a sequence of air highways that minimizes the cost of flying from an origin to any destination.
Edit intent: coherence
Original:  For the air highway placement problem, we use the flexible and efficient fast marching method to solve the Eikonal equation, which produces a sequence of air highways that minimizes the cost of flying from an origin to any destination.
Revised:  For the air highway placement problem, we use the flexible and efficient fast marching method is used to produce a sequence of air highways that minimizes the cost of flying from an origin to any destination.
Edit intent: coherence
Original:  Within the platoons that travel on the air highways, we model each vehicle as a hybrid system with modes corresponding to its role in the platoon .
Revised:  Within the platoons that travel on the air highways, each vehicle is modeled as a hybrid system with modes corresponding to its role in the platoon .
Edit intent: style
Original:  Within the platoons that travel on the air highways, we model each vehicle as a hybrid system with modes corresponding to its role in the platoon .
Revised:  Within the platoons that travel on the air highways, we model each vehicle as a hybrid system .
Edit intent: clarity
Original:  Using Hamilton-Jacobi reachability, we propose several liveness controllers and a safety controller that guarantee the success and safety of all mode transitions.
Revised:  Using Hamilton-Jacobi reachability, safety and liveness are guaranteed for all mode transitions.
Edit intent: clarity
Original:  For a single altitude range, our approach guarantees safety for one safety breach per vehicle;
Revised:  For a single altitude range, the proposed approach guarantees safety for one safety breach per vehicle;
Edit intent: clarity
Original:  We demonstrate the satisfaction of liveness and safety requirements through simulations of three common scenarios.
Revised:  The satisfaction of safety and liveness requirements is demonstrated through simulations of three common scenarios.
Edit intent: clarity
Original:  We demonstrate the satisfaction of liveness and safety requirements through simulations of three common scenarios.
Revised:  We demonstrate the satisfaction of liveness and safety requirements through simulations of three scenarios.
Edit intent: clarity
Original:  As a result, unmanned aerial systems traffic management is needed to ensure the safety and liveness of potentially thousands of UAVs flying simultaneously.
Revised:  As a result, unmanned aerial systems traffic management is needed to ensure the safety and goal satisfaction of potentially thousands of UAVs flying simultaneously.
Edit intent: clarity
Original:  Currently, the analysis of large multi-agent systems cannot tractably provide safety and liveness guarantees if the agents' set of maneuvers is unrestricted.
Revised:  Currently, the analysis of large multi-agent systems cannot tractably provide these guarantees if the agents' set of maneuvers is unrestricted.
Edit intent: clarity
Original:  Using Hamilton-Jacobi reachability, safety and liveness are guaranteed for all mode transitions.
Revised:  Using Hamilton-Jacobi reachability, safety and goal satisfaction are guaranteed for all mode transitions.
Edit intent: clarity
Original:  The satisfaction of safety and liveness requirements is demonstrated through simulations of three  scenarios.
Revised:  We demonstrate the platooning concept through simulations of three scenarios.
Edit intent: clarity
Original:  The satisfaction of safety and liveness requirements is demonstrated through simulations of three  scenarios.
Revised:  The satisfaction of safety and liveness requirements is demonstrated through simulations of three representative scenarios.
Edit intent: clarity
Original:  For a single altitude range, the proposed approach guarantees safety for one safety breach per vehicle ;
Revised:  For a single altitude range, the proposed approach guarantees safety for one safety breach per vehicle ,
Edit intent: fluency
Original:  Each result has a very compelling take-away message: 1. Fast \Delta-coloring of trees requires random bits: Building on the recent lower bounds of Brandt et al. 11 , we prove that the randomized complexity of \Delta-coloring a tree with maximum degree \Delta\ge 55 is \Theta(\log_\Delta\log n), whereas its deterministic complexity is \Theta(\log_\Delta n) for any \Delta\ge 3.
Revised:  Each result has a very compelling take-away message: 1. Fast \Delta-coloring of trees requires random bits: Building on the recent lower bounds of Brandt et al. , we prove that the randomized complexity of \Delta-coloring a tree with maximum degree \Delta\ge 55 is \Theta(\log_\Delta\log n), whereas its deterministic complexity is \Theta(\log_\Delta n) for any \Delta\ge 3.
Edit intent: coherence
Original:  2. Randomized lower bounds imply deterministic lower bounds: We prove that any deterministic algorithm for a natural class of problems that runs in O(1)+o(\log_\Delta n) rounds can be transformed to run in O(\log^* n - \log^*\Delta+1) rounds.
Revised:  2. Randomized lower bounds imply deterministic lower bounds: We prove that any deterministic algorithm for a natural class of problems that runs in O(1)+o(\log_\Delta n) rounds can be transformed to run in O(\log^* n- \log^*\Delta+1) rounds.
Edit intent: fluency
Original: Current deep learning architectures are growing larger in order to learn from enormous datasets.
Revised: Current deep learning architectures are growing larger in order to learn from complex datasets.
Edit intent: clarity
Original:  We present a novel technique to reduce the amount of computation needed to train and test deep net-works drastically .
Revised:  We present a novel technique to reduce the amount of computation needed to train and test deep networks .
Edit intent: clarity