wanyu/IteraTeR_v2 huggingface dataset:
Original:  Our communication complexity result allows us to get lower bound for k-QOBDD and  hierarchies for sublinear width bounded error k-QOBDDs, for k=o(\sqrt{n}).
Revised:  Our communication complexity result allows us to get lower bound for k-QOBDD and hierarchies for sublinear width bounded error k-QOBDDs, where k=o(\sqrt{n}).
Edit intent: clarity
Original:  Also we prove a hierarchy for polynomial size bounded error k-QOBDDs for constant k , and it differs from the situation with  unbounded error where it is known that increasing of k does not give any advantage.
Revised:  Furthermore, we prove a hierarchy for polynomial size bounded error k-QOBDDs for constant k , and it differs from the situation with unbounded error where it is known that increasing of k does not give any advantage.
Edit intent: coherence
Original:  Also we prove a hierarchy for polynomial size bounded error k-QOBDDs for constant k , and it differs from the situation with  unbounded error where it is known that increasing of k does not give any advantage.
Revised:  Also we prove a hierarchy for polynomial size bounded error k-QOBDDs for constant k . This result differs from the situation with unbounded error where it is known that increasing of k does not give any advantage.
Edit intent: clarity
Original:  Also we prove a hierarchy for polynomial size bounded error k-QOBDDs for constant k , and it differs from the situation with  unbounded error where it is known that increasing of k does not give any advantage.
Revised:  Also we prove a hierarchy for polynomial size bounded error k-QOBDDs for constant k , and it differs from the situation with an unbounded error where it is known that increasing of k does not give any advantage.
Edit intent: fluency
Original:  Also we prove a hierarchy for polynomial size bounded error k-QOBDDs for constant k , and it differs from the situation with  unbounded error where it is known that increasing of k does not give any advantage.
Revised:  Also we prove a hierarchy for polynomial size bounded error k-QOBDDs for constant k , and it differs from the situation with unbounded error where it is known that an increase of k does not give any advantage.
Edit intent: fluency
Original: We introduce Fonduer, a knowledge base construction (KBC) framework for richly formatted information extraction (RFIE), where entity relations and attributes are conveyed via structural, tabular, visual, and textual expressions.
Revised: We focus on knowledge base construction (KBC) framework for richly formatted information extraction (RFIE), where entity relations and attributes are conveyed via structural, tabular, visual, and textual expressions.
Edit intent: coherence
Original: We introduce Fonduer, a knowledge base construction (KBC) framework for richly formatted information extraction (RFIE), where entity relations and attributes are conveyed via structural, tabular, visual, and textual expressions.
Revised: We introduce Fonduer, a knowledge base construction (KBC) from richly formatted data. In contrast to KBC from text or tabular data, KBC from richly formatted data aims to extract relations conveyed jointly via textual, structural, tabular, visual, and textual expressions.
Edit intent: clarity
Original:  In some domains, our users have produced up to 1.87x the number of correct entires compared to expert-curated public knowledge bases.
Revised:  In some domains, our users have produced up to 1.87x the number of correct entries---compared to expert-curated public knowledge bases.
Edit intent: fluency
Original: We present a simple distributed algorithm that, given a regular graph consisting of two communities (or clusters),each inducing a good expander and such that the cut between them has sparsity\pm 1 /\mbox{polylog(n), recovers the two communities.
Revised: We present a simple distributed algorithm that, given a regular graph consisting of two communities (or clusters),each inducing a good expander and such that the cut between them has sparsity\pm 1 (n), recovers the two communities.
Edit intent: clarity
Original: Consider the following probabilistic process on a graph G =(V, E) . After initially labeling each vertex v by a real number, say randomly chosen in \pm 1 , we repeatedly pick a random edge and replace the values of its endpoints by their average.
Revised: Consider the following asynchronous, opportunistic communication model over a graph G =(V, E) . After initially labeling each vertex v by a real number, say randomly chosen in \pm 1 , we repeatedly pick a random edge and replace the values of its endpoints by their average.
Edit intent: clarity
Original: Consider the following probabilistic process on a graph G =(V, E) . After initially labeling each vertex v by a real number, say randomly chosen in \pm 1 , we repeatedly pick a random edge and replace the values of its endpoints by their average.
Revised: Consider the following probabilistic process on a graph G =(V, E) . After initially labeling each vertex v by a real number, say \pm 1 , we repeatedly pick a random edge and replace the values of its endpoints by their average.
Edit intent: clarity
Original:  Suppose the process is run on a graph exhibiting a community structure , such as two expanders joined by a sparse cut :%DIFDELCMD < {\em %%% is there a phase of the process, in which its state reflects the underlying community structure?
Revised:  Suppose the process is run on a graph exhibiting a community structure , such as two expanders joined by a sparse cut %DIFDELCMD < {\em %%% is there a phase of the process, in which its state reflects the underlying community structure?
Edit intent: fluency
Original:  This results in the first asynchronous distributed algorithms that require logarithmic or polylogarithmic work per node (depending on the sparsity of the cut) and that approximately recover community structure .
Revised:  This results in the first opportunistic protocols that approximately recover community structure using only polylogarithmic work per node (depending on the sparsity of the cut) and that approximately recover community structure .
Edit intent: clarity
Original:  Our evaluation results and code are available on-line at URL clustering
Revised:  Our evaluation results and code are available on-line at URL 
Edit intent: clarity
Original:  In earlier work, Esparza and Desel have shown that deciding soundness of a negotiation is PSPACE-complete , and in PTIME if the negotiation is deterministic.
Revised:  In earlier work, Esparza and Desel have shown that deciding soundness of a negotiation is Pspace-complete , and in PTIME if the negotiation is deterministic.
Edit intent: fluency
Original:  In earlier work, Esparza and Desel have shown that deciding soundness of a negotiation is PSPACE-complete , and in PTIME if the negotiation is deterministic.
Revised:  In earlier work, Esparza and Desel have shown that deciding soundness of a negotiation is PSPACE-complete , and in Ptime if the negotiation is deterministic.
Edit intent: fluency
Original:  In the first part of this paper we revisit the soundness problem for deterministic negotiations, and show that it is NLOGSPACE-complete , improving on the earlier algorithm, which requires linear space.
Revised:  In the first part of this paper we revisit the soundness problem for deterministic negotiations, and show that it is Nlogspace-complete , improving on the earlier algorithm, which requires linear space.
Edit intent: fluency
Original:  We prove that the soundness problem can be solved in polynomial time for acyclic, weakly non-deterministic negotiations, a more general class than the one considered by them.
Revised:  We prove that the soundness problem can be solved in polynomial time for acyclic, weakly non- deterministic negotiations, a more general class than the one considered by them.
Edit intent: fluency
Original: The evident robustness of neural computation is hypothesized to arise from some degree of local stability around dynamically-generated sequences of local-circuit activity states involving many neurons.
Revised: Synaptic interactions structure the phase space of the dynamics of neural circuits and constrain neural computation. Understanding how requires methods that handle those discrete interactions, yet few exist.
Edit intent: clarity
Original:   We find that the basin boundaries are the pre-images of future spike-time collision events.
Revised:  We find that the basin boundaries are the pre-images of spike-time collision events.
Edit intent: clarity
Original:  Formulating the corresponding event statistics , we derive expressions for the rate of divergence of neighboring basins and  their size distribution.
Revised:  Formulating the corresponding event statistics , we derive expressions for the rate of divergence of neighboring basins and for their size distribution.
Edit intent: fluency
Original:  The average basin diameter grows with the inhibitory coupling strength and shrinks with the rate of spike events.
Revised:  This theory reveals that the typical basin diameter grows with the inhibitory coupling strength and shrinks with the rate of spike events.
Edit intent: clarity
Original:  The average basin diameter grows with the inhibitory coupling strength and shrinks with the rate of spike events.
Revised:  The average basin diameter grows with inhibitory coupling strength and shrinks with the rate of spike events.
Edit intent: fluency
Original:  Our work provides a global picture of the phase-space of a local-circuit model, contributing to the understanding of its collective dynamics and function .
Revised:  Our study provides an analytical and generalizable approach for dissecting how connectivity, coupling strength, single neuron dynamics and population activity shape the phase space geometry of spiking circuits .
Edit intent: clarity
Original: A set system \mathcal{F \subseteq } \ge 2 ^{[n] shatters a given set S \subseteq }%DIFDELCMD < [%%% n if \{F\cap S : F \in \mathcal{F \}=} \ge \ge 2 ^S, and \mathrm{Sh n%DIFDELCMD < ]%%% ;
Revised:  \subseteq } \ge 2 ^{[n] shatters a given set S \subseteq }%DIFDELCMD < [%%% n if \{F\cap S : F \in \mathcal{F \}=} \ge \ge 2 ^S, and \mathrm{Sh n%DIFDELCMD < ]%%% ;
Edit intent: clarity
Original: A set system \mathcal{F \subseteq } \ge 2 ^{[n] shatters a given set S \subseteq }%DIFDELCMD < [%%% n if \{F\cap S : F \in \mathcal{F \}=} \ge \ge 2 ^S, and \mathrm{Sh n%DIFDELCMD < ]%%% ;
Revised: A set system \mathcal{F \subseteq } \ge 2 shatters a given set S \subseteq }%DIFDELCMD < [%%% n if \{F\cap S : F \in \mathcal{F \}=} \ge \ge 2 ^S, and \mathrm{Sh n%DIFDELCMD < ]%%% ;
Edit intent: coherence
Original: A set system \mathcal{F \subseteq } \ge 2 ^{[n] shatters a given set S \subseteq }%DIFDELCMD < [%%% n if \{F\cap S : F \in \mathcal{F \}=} \ge \ge 2 ^S, and \mathrm{Sh n%DIFDELCMD < ]%%% ;
Revised: A set system \mathcal{F \subseteq } \ge 2 ^{[n] shatters a given set S \subseteq }%DIFDELCMD < [%%% if \{F\cap S : F \in \mathcal{F \}=} \ge \ge 2 ^S, and \mathrm{Sh n%DIFDELCMD < ]%%% ;
Edit intent: fluency
Original: A set system \mathcal{F \subseteq } \ge 2 ^{[n] shatters a given set S \subseteq }%DIFDELCMD < [%%% n if \{F\cap S : F \in \mathcal{F \}=} \ge \ge 2 ^S, and \mathrm{Sh n%DIFDELCMD < ]%%% ;
Revised: A set system \mathcal{F \subseteq } \ge 2 ^{[n] shatters a given set S \subseteq }%DIFDELCMD < [%%% n if \{F\cap S : F \in \mathcal{F \}=} \ge t\ge 2 ^S, and \mathrm{Sh n%DIFDELCMD < ]%%% ;
Edit intent: fluency
Original: A set system \mathcal{F \subseteq } \ge 2 ^{[n] shatters a given set S \subseteq }%DIFDELCMD < [%%% n if \{F\cap S : F \in \mathcal{F \}=} \ge \ge 2 ^S, and \mathrm{Sh n%DIFDELCMD < ]%%% ;
Revised: A set system \mathcal{F \subseteq } \ge 2 ^{[n] shatters a given set S \subseteq }%DIFDELCMD < [%%% n if \{F\cap S : F \in \mathcal{F \}=} \ge \ge 2 ^S, and \mathrm{Sh %DIFDELCMD < ]%%% ;
Edit intent: fluency
Original:  t,k} ,  k, m) , the maximum number of k-subsets of n%DIFDELCMD < ] %%% that can be shattered by a set system of size m.
Revised:  t,k} , k, n%DIFDELCMD < ] %%% that can be shattered by a set system of size m.
Edit intent: clarity
Original:  t,k} ,  k, m) , the maximum number of k-subsets of n%DIFDELCMD < ] %%% that can be shattered by a set system of size m.
Revised:  t,k} , k, m) , the maximum number of k-subsets of %DIFDELCMD < ] %%% that can be shattered by a set system of size m.
Edit intent: clarity
Original: We consider the classical complexity of approximately simulating time evolution under spatially local quadratic bosonic Hamiltonians for time t . We obtain upper and lower bounds on the scaling of t with the number of bosons , n , for which simulation, cast as a sampling problem, is classically efficient and provably hard, respectively.
Revised: We make the case for studying the complexity of approximately simulating time evolution under spatially local quadratic bosonic Hamiltonians for time t . We obtain upper and lower bounds on the scaling of t with the number of bosons , n , for which simulation, cast as a sampling problem, is classically efficient and provably hard, respectively.
Edit intent: clarity
Original: We consider the classical complexity of approximately simulating time evolution under spatially local quadratic bosonic Hamiltonians for time t . We obtain upper and lower bounds on the scaling of t with the number of bosons , n , for which simulation, cast as a sampling problem, is classically efficient and provably hard, respectively.
Revised: We consider the classical complexity of approximately simulating time evolution under spatially local quadratic bosonic Hamiltonians . We obtain upper and lower bounds on the scaling of t with the number of bosons , n , for which simulation, cast as a sampling problem, is classically efficient and provably hard, respectively.
Edit intent: clarity
Original: We consider the classical complexity of approximately simulating time evolution under spatially local quadratic bosonic Hamiltonians for time t . We obtain upper and lower bounds on the scaling of t with the number of bosons , n , for which simulation, cast as a sampling problem, is classically efficient and provably hard, respectively.
Revised: We consider the classical complexity of approximately simulating time evolution under spatially local quadratic bosonic Hamiltonians for time t . We obtain an upper bound on the scaling of t with the number of bosons , n , for which simulation, cast as a sampling problem, is classically efficient and provably hard, respectively.
Edit intent: clarity
Original: We consider the classical complexity of approximately simulating time evolution under spatially local quadratic bosonic Hamiltonians for time t . We obtain upper and lower bounds on the scaling of t with the number of bosons , n , for which simulation, cast as a sampling problem, is classically efficient and provably hard, respectively.
Revised: We consider the classical complexity of approximately simulating time evolution under spatially local quadratic bosonic Hamiltonians for time t . We obtain upper and lower bounds on the scaling of t with the number of bosons n for which approximate sampling is classically efficient and provably hard, respectively.
Edit intent: clarity
Original:  ] We view these results in the light of classifying phases of physical systems based on parameters in the Hamiltonian and conjecture a link to dynamical phase transitions .
Revised:  ] We view these results in the light of classifying phases of physical systems based on parameters in the Hamiltonian .
Edit intent: clarity
Original:  This work presents a simple equation linking an arbitrary degree distribution to the corresponding size distribution of connected components.
Revised:  This work presents a simple equation that gives for an arbitrary degree distribution to the corresponding size distribution of connected components.
Edit intent: clarity
Original:  This work presents a simple equation linking an arbitrary degree distribution to the corresponding size distribution of connected components.
Revised:  This work presents a simple equation linking an arbitrary degree distribution the corresponding size distribution of connected components.
Edit intent: fluency
Original:  The analytical analysis reveals that the asymptote of component-size distribution is completely defined by only a few parameters of the degree distribution: the first three moments, scale and exponent (if applicable).
Revised:  The analytical analysis reveals that the asymptote of the component size distribution is completely defined by only a few parameters of the degree distribution: the first three moments, scale and exponent (if applicable).
Edit intent: fluency
Original:  When the degree distribution features a heavy tail, multiple asymptotic modes are observed in the component-size distribution that may or may not feature a heavy tail.
Revised:  When the degree distribution features a heavy tail, multiple asymptotic modes are observed in the component size distribution that, in turn, may or may not feature a heavy tail.
Edit intent: clarity
Original:  One of the major challenges in phylogenetics regards the estimation of the marginal likelihood.
Revised:  One of the major challenges in phylogenetics is the estimation of the marginal likelihood.
Edit intent: clarity
Original:  Another interesting challenge regards the estimation of the posterior distribution.
Revised:  Another interesting challenge relates to the estimation of the posterior distribution.
Edit intent: fluency
Original:  Nested sampling (NS) is a Bayesian  algorithm which provides the means to estimate marginal likelihoods  and to sample from the posterior distribution at no extra cost.
Revised:  Nested sampling (NS) is a Bayesian computation algorithm which provides the means to estimate marginal likelihoods and to sample from the posterior distribution at no extra cost.
Edit intent: clarity
Original:  We conclude that NS is a very competitive and attractive algorithm for phylogenetic inference  .
Revised:  We conclude that NS is a competitive and attractive algorithm for phylogenetic inference .
Edit intent: clarity
Original:  In general, these algorithms require a high computational effort to yield reliable inferences .
Revised:  In general, these algorithms require a high computational effort to yield reliable estimates .
Edit intent: clarity
Original:  The methods currently used in phylogenetics for marginal likelihood estimation lack of practicality due to their dependence on many tuning parameters and their incapacity to provide a direct way to calculate the uncertainties associated with the estimates , unlike NS. In this paper , we introduce NS to phylogenetics.
Revised:  The methods currently used in phylogenetics for marginal likelihood estimation lack in practicality due to their dependence on many tuning parameters and their incapacity to provide a direct way to calculate the uncertainties associated with the estimates , unlike NS. In this paper , we introduce NS to phylogenetics.
Edit intent: fluency
Original:  The methods currently used in phylogenetics for marginal likelihood estimation lack of practicality due to their dependence on many tuning parameters and their incapacity to provide a direct way to calculate the uncertainties associated with the estimates , unlike NS. In this paper , we introduce NS to phylogenetics.
Revised:  The methods currently used in phylogenetics for marginal likelihood estimation lack of practicality due to their dependence on many tuning parameters and their incapacity to provide a direct way to calculate the uncertainties associated with the estimates . To address these issues , we introduce NS to phylogenetics.
Edit intent: clarity
Original:  Its performance is analysed under different scenarios and compared to established methods.
Revised:  Its performance is assessed under different scenarios and compared to established methods.
Edit intent: fluency
Original:  An implementation is available as a package for BEAST 2 , available from URL under the LGPL licence .
Revised:  An implementation is available as a package for BEAST 2 under the LGPL licence .
Edit intent: clarity
Original: Steganography is collection of methods to hide secret information ("payload") within non-secret information ( "container").
Revised: Steganography is collection of methods to hide secret information ("payload") within non-secret information "container").
Edit intent: fluency
Original: We consider social welfare functions that satisfy Arrow's classic axioms of independence of irrelevant alternatives and Pareto optimality when individual and collective preferences are  continuous and convex .
Revised: We consider social welfare functions that satisfy Arrow's classic axioms of independence of irrelevant alternatives and Pareto optimality when individual and collective preferences are assumed to be continuous and convex .
Edit intent: clarity
Original:  These assumptions are sufficient for the existence of maximal elements and the choice consistency of functions that return these elements  .
Revised:  These assumptions are sufficient for the existence of maximal elements and the consistency of choice functions that return these elements .
Edit intent: fluency
Original:  The domains allow for arbitrary preferences over pure outcomes , which in turn completely determine an agent's preferences over all remaining outcomes.
Revised:  The domains allow for arbitrary preferences over alternatives , which in turn completely determine an agent's preferences over all remaining outcomes.
Edit intent: clarity
Original:  The domains allow for arbitrary preferences over pure outcomes , which in turn completely determine an agent's preferences over all remaining outcomes.
Revised:  The domains allow for arbitrary preferences over pure outcomes , which in turn completely determine an agent's preferences over all outcomes.
Edit intent: clarity
Original:  The only Arrovian social welfare functions on these domains constitute an intriguing combination of utilitarianism and pairwiseness.
Revised:  The only Arrovian social welfare functions on these domains constitute an interesting combination of utilitarianism and pairwiseness.
Edit intent: fluency
Original:  When also assuming anonymity, Arrow's impossibility turns into a complete characterization of a unique desirable social welfare function  .
Revised:  When also assuming anonymity, Arrow's impossibility turns into a complete characterization of a unique social welfare function .
Edit intent: clarity
Original:  We provide characterizations of both the domains of preferences and the social welfare functions that allow for  Arrovian aggregation.
Revised:  We provide characterizations of both the domains of preferences and the social welfare functions that allow for anonymous Arrovian aggregation.
Edit intent: clarity
Original:  The domains allow for arbitrary preferences over alternatives, which in turn completely determine an agent's preferences over all outcomes.
Revised:  The domains admit arbitrary preferences over alternatives, which in turn completely determine an agent's preferences over all outcomes.
Edit intent: clarity
Original:  When also assuming anonymity , Arrow's impossibility turns into a complete characterization of a unique social welfare function, which can be readily applied in settings that allow for lotteries or divisible resources such as time or money.
Revised:  When also assuming anonymity , Arrow's impossibility turns into a complete characterization of a unique social welfare function, which can be readily applied in settings involving divisible resources such as time or money.
Edit intent: clarity
Original:  When also assuming anonymity , Arrow's impossibility turns into a complete characterization of a unique social welfare function, which can be readily applied in settings that allow for lotteries or divisible resources such as time or money.
Revised:  When also assuming anonymity , Arrow's impossibility turns into a complete characterization of a unique social welfare function, which can be readily applied in settings that allow for lotteries or divisible resources such as probability, time, or money.
Edit intent: clarity