wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Informally, our definition captures the idea that an agent should not experience a large change in their utility as long as they make " small" or " innocuous" mistakes while reporting their preferences . We study thisnotion in the context of fair and efficient allocations of indivisible goods among two agents , and show that it is impossible to achieve exact stability along with even a weak notion of fairness and even approximate efficiency.
Revised:  Informally, our definition captures the idea that an agent should not experience a large change in their utility as long as they make " small" or " innocuous" mistakes while reporting their preferences to experience a large change in their utility for the final outcome. To address this, we introduce a notion of algorithmic stability and study it in the context of fair and efficient allocations of indivisible goods among two agents , and show that it is impossible to achieve exact stability along with even a weak notion of fairness and even approximate efficiency.
Edit intent: meaning-changed
Original:  We study thisnotion in the context of fair and efficient allocations of indivisible goods among two agents , and show that it is impossible to achieve exact stability along with even a weak notion of fairness and even approximate efficiency.
Revised:  We study thisnotion in the context of fair and efficient allocations of indivisible goods among two agents . We show that it is impossible to achieve exact stability along with even a weak notion of fairness and even approximate efficiency.
Edit intent: coherence
Original:  Towards this end  we present a general characterization result for pairwise maximin share allocations, and in turn use it to design an algorithm that is approximately-stable and guarantees a pairwise maximin share and Pareto optimal allocation for two agents.
Revised:  Towards this end , we present a general characterization result for pairwise maximin share allocations, and in turn use it to design an algorithm that is approximately-stable and guarantees a pairwise maximin share and Pareto optimal allocation for two agents.
Edit intent: fluency
Original:  Herein, we analyze the synchronous k-Majority dynamics, where nodes sample k neighbors uniformly at random with replacement and adopt the majority state among the nodes in the sample ( potential ties are broken uniformly at random).
Revised:  Herein, we analyze the synchronous k-Majority dynamics, where in each discrete-time round nodes simultaneously sample k neighbors uniformly at random with replacement and adopt the majority state among the nodes in the sample ( potential ties are broken uniformly at random).
Edit intent: meaning-changed
Original:  Herein, we analyze the synchronous k-Majority dynamics, where nodes sample k neighbors uniformly at random with replacement and adopt the majority state among the nodes in the sample ( potential ties are broken uniformly at random).
Revised:  Herein, we analyze the synchronous k-Majority dynamics, where nodes sample k neighbors uniformly at random with replacement and adopt the majority state among the nodes in the sample ( breaking ties uniformly at random).
Edit intent: clarity
Original:  This class of dynamics generalizes other well-known dynamics, e. g., Voter and 3-Majority, which have been studied in the literature as distributed algorithms for consensus .
Revised:  Differently from previous work, we study the robustness of the k-Majority in maintaining a majority, that we consider \mathcal{R g., Voter and 3-Majority, which have been studied in the literature as distributed algorithms for consensus .
Edit intent: meaning-changed
Original:  We consider a biased communication model: whenever nodes sample a neighbor they see state \sigma with some probability p, regardless of the state of the sampled node, and its true state with probability 1-p. Differently from previous works where specific graph topologies are considered, our analysis only requires the graphs to be sufficiently dense, i.e., to have minimum degree \omega(\log n), without any further topological assumption. In this setting we prove two phase transition phenomena, both occurring with high probability, depending on the bias p and on the initial unbalance toward state \sigma.
Revised:  We consider an external agent that wants to subvert the initial majority and, in each round, either tries to alter the communication between each pair of nodes transmitting state \mathcal{B and on the initial unbalance toward state \sigma.
Edit intent: meaning-changed
Original:  In this setting we prove two phase transition phenomena, both occurring with high probability, depending on the bias p and on the initial unbalance toward state \sigma. More in detail,  we prove that for every k \geq 3 \geq3 there exists a p_k^\star such that if p>p _k^\star the process reaches in O(1) rounds a \sigma-almost-consensus, i.e., a configuration where a fraction 1-o(1) of the volume is in state \sigma.
Revised:  In this setting we prove two phase transition phenomena, both occurring with high probability, depending on the bias p and on the same critical value. By considering initial configurations in which each node has probability q \in (\frac{1 we prove that for every k \geq 3 \geq3 there exists a p_k^\star such that if p>p _k^\star the process reaches in O(1) rounds a \sigma-almost-consensus, i.e., a configuration where a fraction 1-o(1) of the volume is in state \sigma.
Edit intent: meaning-changed
Original:  More in detail,  we prove that for every k \geq 3 \geq3 there exists a p_k^\star such that if p>p _k^\star the process reaches in O(1) rounds a \sigma-almost-consensus, i.e., a configuration where a fraction 1-o(1) of the volume is in state \sigma.
Revised:  More in detail, of being in state \mathcal{R we prove that for every k \geq 3 \geq3 there exists a p_k^\star such that if p>p _k^\star the process reaches in O(1) rounds a \sigma-almost-consensus, i.e., a configuration where a fraction 1-o(1) of the volume is in state \sigma.
Edit intent: meaning-changed
Original:  More in detail,  we prove that for every k \geq 3 \geq3 there exists a p_k^\star such that if p>p _k^\star the process reaches in O(1) rounds a \sigma-almost-consensus, i.e., a configuration where a fraction 1-o(1) of the volume is in state \sigma.
Revised:  More in detail, we prove that for every k \geq3 there exists a p_k^\star such that if p>p _k^\star the process reaches in O(1) rounds a \sigma-almost-consensus, i.e., a configuration where a fraction 1-o(1) of the volume is in state \sigma.
Edit intent: meaning-changed
Original:  More in detail,  we prove that for every k \geq 3 \geq3 there exists a p_k^\star such that if p>p _k^\star the process reaches in O(1) rounds a \sigma-almost-consensus, i.e., a configuration where a fraction 1-o(1) of the volume is in state \sigma.
Revised:  More in detail, we prove that for every k \geq 3 \geq3 there exists a critical value p_{k,q if p>p _k^\star the process reaches in O(1) rounds a \sigma-almost-consensus, i.e., a configuration where a fraction 1-o(1) of the volume is in state \sigma.
Edit intent: meaning-changed
Original:  More in detail,  we prove that for every k \geq 3 \geq3 there exists a p_k^\star such that if p>p _k^\star the process reaches in O(1) rounds a \sigma-almost-consensus, i.e., a configuration where a fraction 1-o(1) of the volume is in state \sigma. On the other hand, if p < p_k^\star, we look at random initial configurations in which every node is in state \sigma with probability 1-q independently of the others.
Revised:  More in detail, we prove that for every k \geq 3 \geq3 there exists a p_k^\star such that if p>p _{k,q < p_k^\star, we look at random initial configurations in which every node is in state \sigma with probability 1-q independently of the others.
Edit intent: meaning-changed
Original:  On the other hand, if p < p_k^\star, we look at random initial configurations in which every node is in state \sigma with probability 1-q independently of the others. We prove that there exists a constant q_{p,k^\star such that if q < q\SUBSCRIPT}%DIFDELCMD < {%%% p , k ^\star then a \sigma-almost-consensus is still reached in O(1) rounds, while, if q > q _{p,k^\star, the process spends n^{\omega(1)} rounds in a metastable phase where the fraction of volume in state \sigma is around a constant value depending only on p and k}  .
Revised:  On the other hand, if p < ^\star such that if q < q\SUBSCRIPT}%DIFDELCMD < {%%% p , k ^\star then a \sigma-almost-consensus is still reached in O(1) rounds, while, if q > q _{p,k^\star, the process spends n^{\omega(1)} rounds in a metastable phase where the fraction of volume in state \sigma is around a constant value depending only on p and k} .
Edit intent: coherence
Original:  We prove that there exists a constant q_{p,k^\star such that if q < q\SUBSCRIPT}%DIFDELCMD < {%%% p , k ^\star then a \sigma-almost-consensus is still reached in O(1) rounds, while, if q > q _{p,k^\star, the process spends n^{\omega(1)} rounds in a metastable phase where the fraction of volume in state \sigma is around a constant value depending only on p and k}  .
Revised:  We prove that there exists a constant q_{p,k^\star such that if q < q\SUBSCRIPT}%DIFDELCMD < {%%% p \SUBSCRIPT k ^\star then a \sigma-almost-consensus is still reached in O(1) rounds, while, if q > q _{p,k^\star, the process spends n^{\omega(1)} rounds in a metastable phase where the fraction of volume in state \sigma is around a constant value depending only on p and k} .
Edit intent: fluency
Original:  We prove that there exists a constant q_{p,k^\star such that if q < q\SUBSCRIPT}%DIFDELCMD < {%%% p , k ^\star then a \sigma-almost-consensus is still reached in O(1) rounds, while, if q > q _{p,k^\star, the process spends n^{\omega(1)} rounds in a metastable phase where the fraction of volume in state \sigma is around a constant value depending only on p and k}  .
Revised:  We prove that there exists a constant q_{p,k^\star such that if q < q\SUBSCRIPT}%DIFDELCMD < {%%% p , k , q _{p,k^\star, the process spends n^{\omega(1)} rounds in a metastable phase where the fraction of volume in state \sigma is around a constant value depending only on p and k} .
Edit intent: clarity
Original:  We prove that there exists a constant q_{p,k^\star such that if q < q\SUBSCRIPT}%DIFDELCMD < {%%% p , k ^\star then a \sigma-almost-consensus is still reached in O(1) rounds, while, if q > q _{p,k^\star, the process spends n^{\omega(1)} rounds in a metastable phase where the fraction of volume in state \sigma is around a constant value depending only on p and k}  .
Revised:  We prove that there exists a constant q_{p,k^\star such that if q < q\SUBSCRIPT}%DIFDELCMD < {%%% p , k ^\star then a \sigma-almost-consensus is still reached in O(1) rounds, while, if q > q ^\star, the process spends n^{\omega(1)} rounds in a metastable phase where the fraction of volume in state \sigma is around a constant value depending only on p and k} .
Edit intent: clarity
Original:  We prove that there exists a constant q_{p,k^\star such that if q < q\SUBSCRIPT}%DIFDELCMD < {%%% p , k ^\star then a \sigma-almost-consensus is still reached in O(1) rounds, while, if q > q _{p,k^\star, the process spends n^{\omega(1)} rounds in a metastable phase where the fraction of volume in state \sigma is around a constant value depending only on p and k}  .
Revised:  We prove that there exists a constant q_{p,k^\star such that if q < q\SUBSCRIPT}%DIFDELCMD < {%%% p , k ^\star then a \sigma-almost-consensus is still reached in O(1) rounds, while, if q > q _{p,k^\star, the process spends n^{\omega(1)} rounds in a metastable phase where the fraction of volume in state \sigma is around a constant value depending only on p and k} ^*, the external agent needs at least a superpolynomial number of rounds to subvert the initial majority .
Edit intent: meaning-changed
Original: Two  point configurations \{p_1,\ldots,p_n\} and \{q_1,\ldots,q_n\} are of the same order type if, for every i,j,k, the triples (p_i,p_j,p_k) and (q_i,q_j,q_k) have the same orientation.
Revised: Two labeled point configurations \{p_1,\ldots,p_n\} and \{q_1,\ldots,q_n\} are of the same order type if, for every i,j,k, the triples (p_i,p_j,p_k) and (q_i,q_j,q_k) have the same orientation.
Edit intent: meaning-changed
Original:  In 2018, Caraballo, D\'iaz-B\'a{\~n}ez, Fabila-Monroy, Hidalgo-Toscano, Lea{\~n}os, Montejano showed that n ^{ 3n-o (n)} order types can be realized on an integer grid of polynomial size.
Revised:  In 2018, Caraballo, D\'iaz-B\'a{\~n}ez, Fabila-Monroy, Hidalgo-Toscano, Lea{\~n}os, Montejano showed that at least n ^{ 3n-o (n)} order types can be realized on an integer grid of polynomial size.
Edit intent: clarity
Original:  In 2018, Caraballo, D\'iaz-B\'a{\~n}ez, Fabila-Monroy, Hidalgo-Toscano, Lea{\~n}os, Montejano showed that n ^{ 3n-o (n)} order types can be realized on an integer grid of polynomial size.
Revised:  In 2018, Caraballo, D\'iaz-B\'a{\~n}ez, Fabila-Monroy, Hidalgo-Toscano, Lea{\~n}os, Montejano showed that n ^{ 3n+o (n)} order types can be realized on an integer grid of polynomial size.
Edit intent: meaning-changed
Original:  Every day, the probability of infection of the different individuals is updated making use of the stochastic model of the phenomenon and of the information collected in the previous day . Simulations for a closed community of 10000 individuals show that the proposed technique, coupled with a selective confinement policy, can reduce the spread of the disease while limiting the number of individuals confined if compared to random strategies .
Revised:  Every day, the probability of infection of the different individuals is updated making use of the stochastic model of the phenomenon and of the information collected in the previous days . Simulations for a closed community of 10000 individuals show that the proposed technique, coupled with a selective confinement policy, can reduce the spread of the disease while limiting the number of individuals confined if compared to random strategies .
Edit intent: coherence
Original:  Every day, the probability of infection of the different individuals is updated making use of the stochastic model of the phenomenon and of the information collected in the previous day . Simulations for a closed community of 10000 individuals show that the proposed technique, coupled with a selective confinement policy, can reduce the spread of the disease while limiting the number of individuals confined if compared to random strategies .
Revised:  Every day, the probability of infection of the different individuals is updated making use of the stochastic model of the phenomenon and of the information collected in the previous day . Simulations for a closed community of 10000 individuals show that the proposed technique, coupled with a selective confinement policy, can reduce the spread of the disease while limiting the number of individuals confined if compared to the simple contact tracing of positive and to an off-line test selection strategy based on the number of contacts .
Edit intent: meaning-changed
Original:  The fluid mechanics within aeronautical applications, for example, routinely feature rotating (e.g. turbines, wheels and fan blades) or sliding components (e.g. in compressor or turbine cascade simulations).
Revised:  Fluid mechanics within aeronautical applications, for example, routinely feature rotating (e.g. turbines, wheels and fan blades) or sliding components (e.g. in compressor or turbine cascade simulations).
Edit intent: clarity
Original:  Although the mortar approach has  advantages in terms of its numerical properties, in that it preserves the local conservation properties of DG methods, in the context of complex 3D meshes it poses significant implementation difficulties which the point-to-point method handles more readily.
Revised:  Although the mortar approach has significant advantages in terms of its numerical properties, in that it preserves the local conservation properties of DG methods, in the context of complex 3D meshes it poses significant implementation difficulties which the point-to-point method handles more readily.
Edit intent: fluency
Original:  Although the mortar approach has  advantages in terms of its numerical properties, in that it preserves the local conservation properties of DG methods, in the context of complex 3D meshes it poses significant implementation difficulties which the point-to-point method handles more readily.
Revised:  Although the mortar approach has advantages in terms of its numerical properties, in that it preserves the local conservation properties of DG methods, in the context of complex 3D meshes it poses notable implementation difficulties which the point-to-point method handles more readily.
Edit intent: clarity
Original:  In this article we examine the numerical properties of each method, focusing not only on observing convergence orders for smooth solutions, but also how each method performs in under-resolved simulations of linear and nonlinear hyperbolic problems, to inform the use of these methods in implicit large-eddy simulations.
Revised:  In this paper we examine the numerical properties of each method, focusing not only on observing convergence orders for smooth solutions, but also how each method performs in under-resolved simulations of linear and nonlinear hyperbolic problems, to inform the use of these methods in implicit large-eddy simulations.
Edit intent: fluency
Original: We envision a self-sovereign community that defines itself from the grass roots, bottom up, in a decentralized manner. In a different paper we show how a digital community can grow by using a trust graph and maintaining a bound on the number of fake identities. In another paper we show how this trust graph can integrate into a consensus protocol, to maintain a distributed ledger of the history of the community, while maintaining governance over the list of members.
Revised: We envision a self-sovereign community that defines itself from the grass roots, bottom up, decentralized manner, and aim to integrate for it the following previously-proposed building blocks: a mechanism that accepts members into the community while keeping a bounded number of sybils; digital social contracts that define the possible interactions of a community bounded by such a contract; a design for a fault-tolerant distributed ledger implementation of digital social contracts; and a digital social contract for the egalitarian and just minting of the history of the community, while maintaining governance over the list of members.
Edit intent: meaning-changed
Original:  In another paper we show how this trust graph can integrate into a consensus protocol, to maintain a distributed ledger of the history of the community, while maintaining governance over the list of members. Next, we show in this paper how the community can maintain self-sovereignty over the economy, by transferring the role of minting money to the hands of every registered member of the community. Such minting serves both as the origin point of sovereignty over the economy, as well as a form of universal basic income.
Revised:  In another paper we show how this trust graph can integrate into a consensus protocol, to maintain a distributed ledger of digital currency, which also offers a form of universal basic income.
Edit intent: clarity
Original:  Yet, a distributed construction of an online community which is bigger than the reach of personal acquaintances is strongly susceptible to sybils. This paper assumes that the community has some means for occasionally exposing sybils .
Revised:  We augment these building blocks with a mechanism that allows the community to maintain sovereignty over the economy, by making it sybil-resilient. To do so, we assume that the community has some means for occasionally exposing sybils .
Edit intent: meaning-changed
Original:  This paper assumes that the community has some means for occasionally exposing sybils . It then shows, based on this assumption, that there are means to balance back the economy such that all money minted by sybils is eventually retrieved and liquidated, so that - asymptotically - the amount of money minted equals the number of genuine identities , multiplied by the amount of time they were minting.
Revised:  This paper assumes that the community has the means for exposing sybils and we extend the basic egalitarian currency digital social contract with means to balance back the economy such that all money minted by sybils is eventually retrieved and liquidated, so that - asymptotically - the amount of money minted equals the number of genuine identities , multiplied by the amount of time they were minting.
Edit intent: meaning-changed
Original:  It then shows, based on this assumption, that there are means to balance back the economy such that all money minted by sybils is eventually retrieved and liquidated, so that - asymptotically - the amount of money minted equals the number of genuine identities , multiplied by the amount of time they were minting.
Revised:  It then shows, based on this assumption, that there are means to balance the economy so that money minted by sybils is eventually retrieved and liquidated, so that - asymptotically - the amount of money minted equals the number of genuine identities , multiplied by the amount of time they were minting.
Edit intent: clarity
Original:  It then shows, based on this assumption, that there are means to balance back the economy such that all money minted by sybils is eventually retrieved and liquidated, so that - asymptotically - the amount of money minted equals the number of genuine identities , multiplied by the amount of time they were minting.
Revised:  It then shows, based on this assumption, that there are means to balance back the economy such that all money minted by sybils is eventually retrieved and burned. This leads---asymptotically---to distributive justice among the genuine agents, with the amount of money minted equals the number of genuine identities , multiplied by the amount of time they were minting.
Edit intent: meaning-changed
Original:  It then shows, based on this assumption, that there are means to balance back the economy such that all money minted by sybils is eventually retrieved and liquidated, so that - asymptotically - the amount of money minted equals the number of genuine identities , multiplied by the amount of time they were minting.
Revised:  It then shows, based on this assumption, that there are means to balance back the economy such that all money minted by sybils is eventually retrieved and liquidated, so that - asymptotically - the amount of money minted being equal to the number of genuine identities , multiplied by the amount of time they were minting.
Edit intent: clarity
Original:  It then shows, based on this assumption, that there are means to balance back the economy such that all money minted by sybils is eventually retrieved and liquidated, so that - asymptotically - the amount of money minted equals the number of genuine identities , multiplied by the amount of time they were minting.
Revised:  It then shows, based on this assumption, that there are means to balance back the economy such that all money minted by sybils is eventually retrieved and liquidated, so that - asymptotically - the amount of money minted equals the number of genuine agents , multiplied by the amount of time they were minting.
Edit intent: clarity