wanyu/IteraTeR_v2 huggingface dataset:
Original:  Zsid\'o Zsi10 proves an initiality result for simply--typed syntax: given a signature S, the abstract syntax associated to S constitutes the initial object in a category of representations of S in monads.
Revised:  Zsid\'o proves an initiality result for simply--typed syntax: given a signature S, the abstract syntax associated to S constitutes the initial object in a category of representations of S in monads.
Edit intent: clarity
Original:  Zsid\'o Zsi10 proves an initiality result for simply--typed syntax: given a signature S, the abstract syntax associated to S constitutes the initial object in a category of representations of S in monads.
Revised:  Zsid\'o Zsi10 proves an initiality result for simply-typed syntax: given a signature S, the abstract syntax associated to S constitutes the initial object in a category of representations of S in monads.
Edit intent: fluency
Original:  Zsid\'o Zsi10 proves an initiality result for simply--typed syntax: given a signature S, the abstract syntax associated to S constitutes the initial object in a category of representations of S in monads.
Revised:  Zsid\'o Zsi10 proves an initiality result for simply--typed syntax: given a signature S, the abstract syntax associated to S constitutes the initial object in a category of models of S in monads.
Edit intent: clarity
Original:  However, her theorem does only account for translation between two languages over a fixed set of object types .
Revised:  However, her theorem does only account for translation between two languages over a fixed set of object types .
Edit intent: coherence
Original:  We generalize Zsid\'o's notion of representation such that object types may vary, yielding a larger category, while preserving initiality of the syntax therein.
Revised:  We generalize Zsid\'o's notion of model such that object types may vary, yielding a larger category, while preserving initiality of the syntax therein.
Edit intent: clarity
Original:  Thus we obtain an extended initiality theorem for typed abstract syntax, in which translations between terms over different types can be defined via the associated category--theoretic recursion operator as an initial morphism.
Revised:  Thus we obtain an extended initiality theorem for typed abstract syntax, in which translations between terms over different types can be specified via the associated category--theoretic recursion operator as an initial morphism.
Edit intent: clarity
Original:  Thus we obtain an extended initiality theorem for typed abstract syntax, in which translations between terms over different types can be defined via the associated category--theoretic recursion operator as an initial morphism.
Revised:  Thus we obtain an extended initiality theorem for typed abstract syntax, in which translations between terms over different types can be defined via the associated category-theoretic iteration operator as an initial morphism.
Edit intent: clarity
Original:  Our definitions ensure that translations given via initiality are type--safe , i.e. compatible with the typing in the source and target language in the obvious sense.
Revised:  Our definitions ensure that translations specified via initiality are type--safe , i.e. compatible with the typing in the source and target language in the obvious sense.
Edit intent: clarity
Original:  Our definitions ensure that translations given via initiality are type--safe , i.e. compatible with the typing in the source and target language in the obvious sense.
Revised:  Our definitions ensure that translations given via initiality are type-safe , i.e. compatible with the typing in the source and target language in the obvious sense.
Edit intent: fluency
Original: A subgraph H of a graph G is called  spanning, if any vertex of G is not isolated in H, while it is called maximum k-edge-colorable, if H is  k-edge-colorable and contains as many edges as possible .
Revised: A subgraph H of a graph G is called spanning, if any vertex of G is not isolated in H, while it is called maximum k-edge-colorable, if H is proper k-edge-colorable and contains as many edges as possible .
Edit intent: clarity
Original:  We introduce three parameters that are related with spanning k-edge-colorable subgraphs .
Revised:  We introduce three parameters that are related with spanning k-edge-colorable subgraph .
Edit intent: clarity
Original:  We show that \Delta(G) is an upper bound for sp(G), and then we offer a characterization of graphs with sp(G)=\Delta(G).
Revised:  We show that \Delta(G) is an upper bound for sp(G), and then we characterize the class of graphs G that satisfy sp(G)=\Delta(G).
Edit intent: clarity
Original:  The fluid flow in fracture networks with respect to  variation of connectivity patterns is analyzed.
Revised:  The fluid flow in fracture networks with respect to the variation of connectivity patterns is analyzed.
Edit intent: fluency
Original:  Lattice Boltzmann method is used to show  sensitivity of the permeability and fluid velocity distribution to connectivity patterns of generated fracture networks .
Revised:  Lattice Boltzmann method is used to show the sensitivity of the permeability and fluid velocity distribution to connectivity patterns of generated fracture networks .
Edit intent: fluency
Original:  Lattice Boltzmann method is used to show  sensitivity of the permeability and fluid velocity distribution to connectivity patterns of generated fracture networks .
Revised:  Lattice Boltzmann method is used to show sensitivity of the permeability and fluid velocity distribution to synthetic fracture networks' connectivity patterns .
Edit intent: clarity
Original:  Furthermore,  fracture networks are mapped into the graphs  and the characteristics of theses graphs are compared to the main spatial fracture networks.
Revised:  Furthermore, the fracture networks are mapped into the graphs and the characteristics of theses graphs are compared to the main spatial fracture networks.
Edit intent: fluency
Original:  Furthermore,  fracture networks are mapped into the graphs  and the characteristics of theses graphs are compared to the main spatial fracture networks.
Revised:  Furthermore, fracture networks are mapped into the graphs , and the characteristics of theses graphs are compared to the main spatial fracture networks.
Edit intent: fluency
Original:  Furthermore,  fracture networks are mapped into the graphs  and the characteristics of theses graphs are compared to the main spatial fracture networks.
Revised:  Furthermore, fracture networks are mapped into the graphs and the characteristics of these graphs are compared to the main spatial fracture networks.
Edit intent: fluency
Original:  Implemented power law distributions of fracture length -in spatial fracture networks- yield the same node's degree distribution in transformed networks.
Revised:  Implemented power law distributions of fracture length in spatial fracture networks yielded the same node's degree distribution in transformed networks.
Edit intent: fluency
Original:  In the first case, the fractures are embedded in a uniformly distributed fracture sets while the second case covers spatial fracture zones.
Revised:  In the first case, the fractures are embedded in uniformly distributed fracture sets while the second case covers spatial fracture zones.
Edit intent: fluency
Original:  In the first case, the fractures are embedded in a uniformly distributed fracture sets while the second case covers spatial fracture zones.
Revised:  In the first case, the fractures are embedded in a uniformly distributed fracture sets ; the second case covers spatial fracture zones.
Edit intent: coherence
Original:  The abnormal change (transition) in permeability is controlled by  hub growth rate.
Revised:  The abnormal change (transition) in permeability is controlled by the hub growth rate.
Edit intent: fluency
Original:  Also, comparing LBM results with  characteristic mean length of links of transformed networks shows a reverse relationship between the mentioned parameters.
Revised:  Also, comparing LBM results with the characteristic mean length of links of transformed networks shows a reverse relationship between the mentioned parameters.
Edit intent: fluency
Original:  Also, comparing LBM results with  characteristic mean length of links of transformed networks shows a reverse relationship between the mentioned parameters.
Revised:  Also, comparing LBM results with characteristic mean length of transformed networks' links shows a reverse relationship between the mentioned parameters.
Edit intent: fluency
Original:  Also, comparing LBM results with  characteristic mean length of links of transformed networks shows a reverse relationship between the mentioned parameters.
Revised:  Also, comparing LBM results with characteristic mean length of links of transformed networks shows a reverse relationship between the aforementioned parameters.
Edit intent: fluency
Original:  We propose a simple way to significantly accelerate their convergence , based on a careful analysis of the computational cost needed at each iteration  .
Revised:  We propose a simple way to significantly accelerate these schemes , based on a careful analysis of the computational cost needed at each iteration .
Edit intent: clarity
Original: The XOR-satisfiability (XORSAT) problem requires finding an assignment of n Boolean variables that satisfies m exclusive OR (XOR) clauses, whereby each clause constrains a subset of the variables.
Revised: The XOR-satisfiability (XORSAT) problem requires finding an assignment of n Boolean variables that satisfy m exclusive OR (XOR) clauses, whereby each clause constrains a subset of the variables.
Edit intent: fluency
Original:  In particular  we prove that the clustering threshold is sharp and determine its exact location.
Revised:  In particular , we prove that the clustering threshold is sharp and determine its exact location.
Edit intent: fluency
Original: We present a protocol to construct and maintain an overlay on a dynamic peer-to-peer network of maximum size N, in presence of a byzantine adversary controlling a fraction%DIFDELCMD < \bad %%% \leq (\frac{\sqrt{3-1}{2k'})^2-2}%DIFDELCMD < \epsilonof %%% the nodes , for a fixed constant k'>   1 and \epsilon > 0 (not depending on N).
Revised: We %DIFDELCMD < \bad %%% \leq (\frac{\sqrt{3-1}{2k'})^2-2}%DIFDELCMD < \epsilonof %%% the nodes , for a fixed constant k'> 1 and \epsilon > 0 (not depending on N).
Edit intent: clarity
Original: We present a protocol to construct and maintain an overlay on a dynamic peer-to-peer network of maximum size N, in presence of a byzantine adversary controlling a fraction%DIFDELCMD < \bad %%% \leq (\frac{\sqrt{3-1}{2k'})^2-2}%DIFDELCMD < \epsilonof %%% the nodes , for a fixed constant k'>   1 and \epsilon > 0 (not depending on N).
Revised: We present a protocol to construct and maintain an overlay on a dynamic peer-to-peer network of maximum size N, in presence of a byzantine adversary controlling a fraction%DIFDELCMD < \bad %%% \leq (\frac{\sqrt{3-1}{2k'})^2-2}%DIFDELCMD < \epsilonof %%% the nodes , for a fixed constant k'>secure 1 and \epsilon > 0 (not depending on N).
Edit intent: fluency
Original: We present a protocol to construct and maintain an overlay on a dynamic peer-to-peer network of maximum size N, in presence of a byzantine adversary controlling a fraction%DIFDELCMD < \bad %%% \leq (\frac{\sqrt{3-1}{2k'})^2-2}%DIFDELCMD < \epsilonof %%% the nodes , for a fixed constant k'>   1 and \epsilon > 0 (not depending on N).
Revised: We present a protocol to construct and maintain an overlay on a dynamic peer-to-peer network of maximum size N, in presence of a byzantine adversary controlling a fraction%DIFDELCMD < \bad %%% \leq (\frac{\sqrt{3-1}{2k'})^2-2}%DIFDELCMD < \epsilonof %%% the nodes , for a fixed constant k'> and 1 and \epsilon > 0 (not depending on N).
Edit intent: fluency
Original: We present a protocol to construct and maintain an overlay on a dynamic peer-to-peer network of maximum size N, in presence of a byzantine adversary controlling a fraction%DIFDELCMD < \bad %%% \leq (\frac{\sqrt{3-1}{2k'})^2-2}%DIFDELCMD < \epsilonof %%% the nodes , for a fixed constant k'>   1 and \epsilon > 0 (not depending on N).
Revised: We present a protocol to construct and maintain an overlay on a dynamic peer-to-peer network of maximum size N, in presence of a byzantine adversary controlling a fraction%DIFDELCMD < \bad %%% \leq (\frac{\sqrt{3-1}{2k'})^2-2}%DIFDELCMD < \epsilonof %%% the nodes , for a fixed constant k'> scalable 1 and \epsilon > 0 (not depending on N).
Edit intent: fluency
Original: Motivated by recent interest for power grid architectures, we study the relationship between structural features of electrical transmission networks and the behavior of certain dynamical processes taking place in the network.
Edit intent: coherence
Original:  The spectrum of the Laplacian matrix  plays a key role in a wide range of networked dynamical problems , from transient stability analysis  to distributed control  .
Revised:  The spectrum of the Laplacian matrix of a network plays a key role in a wide range of networked dynamical problems , from transient stability analysis to distributed control .
Edit intent: clarity
Original:  The spectrum of the Laplacian matrix  plays a key role in a wide range of networked dynamical problems , from transient stability analysis  to distributed control  .
Revised:  The spectrum of the Laplacian matrix plays a key role in a wide range of dynamical problems associated with the network , from transient stability analysis to distributed control .
Edit intent: clarity
Original:  The spectrum of the Laplacian matrix  plays a key role in a wide range of networked dynamical problems , from transient stability analysis  to distributed control  .
Revised:  The spectrum of the Laplacian matrix plays a key role in a wide range of networked dynamical problems , from transient stability analysis to distributed control of formations .
Edit intent: clarity
Original:  Using methods from algebraic graph theory and convex optimization, we study the relationship between structural features of the network and spectral properties of the Laplacian matrix.
Revised:  Using methods from algebraic graph theory and convex optimization, we study the relationship between structural features of a network and spectral properties of the Laplacian matrix.
Edit intent: fluency
Original:  Using methods from algebraic graph theory and convex optimization, we study the relationship between structural features of the network and spectral properties of the Laplacian matrix.
Revised:  Using methods from algebraic graph theory and convex optimization, we study the relationship between structural features of the network and spectral properties of its Laplacian matrix.
Edit intent: clarity
Original:  We illustrate our results by studying the influence of structural properties on the Laplacian eigenvalues of the American (western states), Spanish and French high-voltage transmission networks  .
Revised:  We illustrate our results by studying the influence of structural properties on the Laplacian eigenvalues of the American (western states), French and Spanish high-voltage transmission networks .
Edit intent: fluency
Original: The spectrum of the Laplacian matrix of a network plays a key role in a wide range of dynamical problems associated with the network, from transient stability analysis of power networks to distributed control of formations.
Edit intent: coherence
Original:  Our study suggests that for such networks the Laplacian  spectral radii and spectral moments are strongly constrained by a particular set of local structural features , namely the degree sequence and the so-called joint-degree distribution .
Revised:  Our study suggests that for such networks the Laplacian spectral moments and spectral radius are strongly constrained by a particular set of local structural features , namely the degree sequence and the so-called joint-degree distribution .
Edit intent: fluency
Original:  Our study suggests that for such networks the Laplacian  spectral radii and spectral moments are strongly constrained by a particular set of local structural features , namely the degree sequence and the so-called joint-degree distribution .
Revised:  Our study suggests that for such networks the Laplacian spectral radii and spectral moments are strongly constrained by local structural features , namely the degree sequence and the so-called joint-degree distribution .
Edit intent: clarity
Original:  Our study suggests that for such networks the Laplacian  spectral radii and spectral moments are strongly constrained by a particular set of local structural features , namely the degree sequence and the so-called joint-degree distribution .
Revised:  Our study suggests that for such networks the Laplacian spectral radii and spectral moments are strongly constrained by a particular set of local structural features of the network .
Edit intent: clarity
Original:  We also show that local structural features are  not enough to characterize the Laplacian spectral gap .
Revised:  We also show that local structural features are not enough to estimate the Laplacian spectral gap .
Edit intent: clarity
Original:  The corresponding superhedging strategy can be obtained going forward in the tree.
Revised:  A corresponding superhedging strategy can be obtained going forward in the tree.
Edit intent: fluency
Original: We study the explicit calculation of the set of superhedging portfolios of contingent claims in a discrete-time market model for d assets with proportional transaction costs when the underlying probability space is finite .
Revised: We study the explicit calculation of the set of superhedging portfolios of contingent claims in a discrete-time market model for d assets with proportional transaction costs .
Edit intent: clarity
Original:  A corresponding superhedging strategy can be obtained going forward in the tree.
Revised:  The corresponding superhedging strategy can be obtained going forward in the tree.
Edit intent: fluency
Original:  We discuss the selection of a trading strategy from the set of all superhedging trading strategies.
Edit intent: coherence
Original: Motivated by the problem of distributed geographical packet forwarding in a wireless sensor network  with sleep-wake cycling nodes, we propose a local forwarding model comprising a node that wishes to forward a packet towards a destination, and a set of next-hop relay nodes , each of which is associated with a reward that summarises the cost/ benefit of forwarding the packet through that relay.
Revised: In geographical forwarding of packets in a large wireless sensor network with sleep-wake cycling nodes, we propose a local forwarding model comprising a node that wishes to forward a packet towards a destination, and a set of next-hop relay nodes , each of which is associated with a reward that summarises the cost/ benefit of forwarding the packet through that relay.
Edit intent: clarity
Original: Motivated by the problem of distributed geographical packet forwarding in a wireless sensor network  with sleep-wake cycling nodes, we propose a local forwarding model comprising a node that wishes to forward a packet towards a destination, and a set of next-hop relay nodes , each of which is associated with a reward that summarises the cost/ benefit of forwarding the packet through that relay.
Revised: Motivated by the problem of distributed geographical packet forwarding in a wireless sensor network (WSN) with sleep-wake cycling nodes, we propose a local forwarding model comprising a node that wishes to forward a packet towards a destination, and a set of next-hop relay nodes , each of which is associated with a reward that summarises the cost/ benefit of forwarding the packet through that relay.
Edit intent: clarity
Original: Motivated by the problem of distributed geographical packet forwarding in a wireless sensor network  with sleep-wake cycling nodes, we propose a local forwarding model comprising a node that wishes to forward a packet towards a destination, and a set of next-hop relay nodes , each of which is associated with a reward that summarises the cost/ benefit of forwarding the packet through that relay.
Revised: Motivated by the problem of distributed geographical packet forwarding in a wireless sensor network with sleep-wake cycling nodes, we are interested in the local decision problem faced by a node that wishes to forward a packet towards a destination, and a set of next-hop relay nodes , each of which is associated with a reward that summarises the cost/ benefit of forwarding the packet through that relay.
Edit intent: clarity
Original: Motivated by the problem of distributed geographical packet forwarding in a wireless sensor network  with sleep-wake cycling nodes, we propose a local forwarding model comprising a node that wishes to forward a packet towards a destination, and a set of next-hop relay nodes , each of which is associated with a reward that summarises the cost/ benefit of forwarding the packet through that relay.
Revised: Motivated by the problem of distributed geographical packet forwarding in a wireless sensor network with sleep-wake cycling nodes, we propose a local forwarding model comprising a node that has custody of a packet and has to choose one among a set of next-hop relay nodes , each of which is associated with a reward that summarises the cost/ benefit of forwarding the packet through that relay.
Edit intent: clarity
Original: Motivated by the problem of distributed geographical packet forwarding in a wireless sensor network  with sleep-wake cycling nodes, we propose a local forwarding model comprising a node that wishes to forward a packet towards a destination, and a set of next-hop relay nodes , each of which is associated with a reward that summarises the cost/ benefit of forwarding the packet through that relay.
Revised: Motivated by the problem of distributed geographical packet forwarding in a wireless sensor network with sleep-wake cycling nodes, we propose a local forwarding model comprising a node that wishes to forward a packet towards a destination, and a set of next-hop relay nodes to forward the packet towards the sink. Each relay is associated with a reward that summarises the cost/ benefit of forwarding the packet through that relay.
Edit intent: clarity
Original: Motivated by the problem of distributed geographical packet forwarding in a wireless sensor network  with sleep-wake cycling nodes, we propose a local forwarding model comprising a node that wishes to forward a packet towards a destination, and a set of next-hop relay nodes , each of which is associated with a reward that summarises the cost/ benefit of forwarding the packet through that relay.
Revised: Motivated by the problem of distributed geographical packet forwarding in a wireless sensor network with sleep-wake cycling nodes, we propose a local forwarding model comprising a node that wishes to forward a packet towards a destination, and a set of next-hop relay nodes , each of which is associated with a reward that summarizes the benefit of forwarding the packet through that relay.
Edit intent: clarity
Original:  Thus, at each relay wake-up instant , the source, given a set of relay reward distributions, has to decide whether to stop (and forward the packet to an already probed relay) , continue waiting for further relays to wake-up , or probe an unprobed relay.
Revised:  Thus, at each relay wake-up instant the forwarder can choose to probe a relay to learn its reward value, based on which the forwarder can then decide whether to stop (and forward the packet to an already probed relay) , continue waiting for further relays to wake-up , or probe an unprobed relay.
Edit intent: clarity
Original:  Thus, at each relay wake-up instant , the source, given a set of relay reward distributions, has to decide whether to stop (and forward the packet to an already probed relay) , continue waiting for further relays to wake-up , or probe an unprobed relay.
Revised:  Thus, at each relay wake-up instant , the source, given a set of relay reward distributions, has to decide whether to stop (and forward its packet to the chosen relay) or to continue to wait for further relays to wake-up , or probe an unprobed relay.
Edit intent: clarity