wanyu/IteraTeR_v2 huggingface dataset:
Original:  An objective and rigorous model, from  'bottom-up' and 'top-down' perspective  is proposed here to  describe the various kinds of context-dependence that we encounter in different branches of biology.
Revised:  An objective and rigorous model, from both 'bottom-up' and 'top-down' perspective is proposed here to describe the various kinds of context-dependence that we encounter in different branches of biology.
Edit intent: clarity
Original:  An objective and rigorous model, from  'bottom-up' and 'top-down' perspective  is proposed here to  describe the various kinds of context-dependence that we encounter in different branches of biology.
Revised:  An objective and rigorous model, from 'bottom-up' as well as 'top-down' perspective is proposed here to describe the various kinds of context-dependence that we encounter in different branches of biology.
Edit intent: clarity
Original:  An objective and rigorous model, from  'bottom-up' and 'top-down' perspective  is proposed here to  describe the various kinds of context-dependence that we encounter in different branches of biology.
Revised:  An objective and rigorous model, from 'bottom-up' and 'top-down' perspective , is proposed here to describe the various kinds of context-dependence that we encounter in different branches of biology.
Edit intent: fluency
Original:  An objective and rigorous model, from  'bottom-up' and 'top-down' perspective  is proposed here to  describe the various kinds of context-dependence that we encounter in different branches of biology.
Revised:  An objective and rigorous model, from 'bottom-up' and 'top-down' perspective is proposed here to serve as the template to describe the various kinds of context-dependence that we encounter in different branches of biology.
Edit intent: clarity
Original:  It is found that a hierarchic nature of dependence amongst the biological contexts models the biological nature best .
Revised:  It is found that a hierarchical nature of dependence amongst the biological contexts models the biological nature best .
Edit intent: fluency
Original: The work presented in this paper addresses the problem of reliable transmission of data through a field of small and vulnerable sensors.
Revised: This paper addresses the problem of reliable transmission of data through a field of small and vulnerable sensors.
Edit intent: clarity
Original:  The scope of this work is to account for the interference impact and the congestion level of the channel to improve the robustness, the delay and the energy consumption of the network with respect to the reference solution known as the GRAB algorithm.
Revised:  The scope of this work is to account for the interference impact and the congestion level of the channel , in order to improve robustness, energy consumption and delay performance, compared to a benchmark routing protocol, the GRAB algorithm.
Edit intent: clarity
Original:  Three solutions are proposed: P-GRAB, a probabilistic routing algorithm that concentrates on interference mitigation, U-GRAB, a utility-based algorithm that adjusts to real-time congestion and UP-GRAB, a combination of P-GRAB and U-GRAB.
Revised:  Three solutions are proposed: P-GRAB, a probabilistic routing algorithm for interference mitigation, U-GRAB, a utility-based algorithm that adjusts to real-time congestion and UP-GRAB, a combination of P-GRAB and U-GRAB.
Edit intent: clarity
Original:  The performance of the three algorithms is investigated and compared to GRAB via simulations.
Edit intent: coherence
Original:  Our approach is to take a holistic view of network management and control that captures the cross-interactions among interference management techniques implemented at various layers of the protocol stack.
Revised:  Our approach is to take a holistic view of the network that captures the cross-interactions among interference management techniques implemented at various layers of the protocol stack.
Edit intent: clarity
Original:  Free-energy calculations can be performed as a function of many collective variables, with a particular focus on biological problems, and using state of the art methods such as metadynamics, umbrella sampling and Jarzynski-equation based steered MD.
Revised:  Free-energy calculations can be performed as a function of many collective variables, with a particular focus on biological problems, and using state-of-the-art methods such as metadynamics, umbrella sampling and Jarzynski-equation based steered MD.
Edit intent: fluency
Original: We present a methodology to extract the backbone of complex networks in which the weight and direction of links, as well as non-topological state variables associated with nodesplay a crucial role.
Revised: We present a methodology to extract the backbone of complex networks based on the weight and direction of links, as well as non-topological state variables associated with nodesplay a crucial role.
Edit intent: clarity
Original:  In this paper, we show how the procedure enables us to address important questions in economics, namely  how control and wealth is structured and concentrated across national markets.
Revised:  In particular, the procedure enables us to address important questions in economics, namely how control and wealth is structured and concentrated across national markets.
Edit intent: coherence
Original:  In this paper, we show how the procedure enables us to address important questions in economics, namely  how control and wealth is structured and concentrated across national markets.
Revised:  In this paper, we show how the procedure enables us to address important questions in economics, namely , how control and wealth is structured and concentrated across national markets.
Edit intent: fluency
Original:  In this paper, we show how the procedure enables us to address important questions in economics, namely  how control and wealth is structured and concentrated across national markets.
Revised:  In this paper, we show how the procedure enables us to address important questions in economics, namely how control and wealth are structured and concentrated across national markets.
Edit intent: fluency
Original:  We report on the first cross-country investigation of ownership networks in the stock markets of 48 countries around the world.
Revised:  We report on the first cross-country investigation of ownership networks , focusing on the stock markets of 48 countries around the world.
Edit intent: clarity
Original:  On the one hand, our analysis confirms results expected on the basis of the literature on corporate control, namely  that in Anglo-Saxon countries control tends to be dispersed among numerous shareholders.
Revised:  On the one hand, our analysis confirms results expected on the basis of the literature on corporate control, namely , that in Anglo-Saxon countries control tends to be dispersed among numerous shareholders.
Edit intent: fluency
Original:  On the other hand, it also reveals that in the same countries, control is found to be highly concentrated at the global level, namely  lying in the hands of very few important shareholders.
Revised:  On the other hand, it also reveals that in the same countries, control is found to be highly concentrated at the global level, namely , lying in the hands of very few important shareholders.
Edit intent: fluency
Original:  This result has previously not been reported , as it is not observable without the kind of network analysis developed here.
Revised:  This result has previously not been reported as they are not observable without the kind of network analysis developed here.
Edit intent: fluency
Original: We study the class of Azema-Yor (AY) processes defined from a general semimartingale with a continuous running supremum process.
Revised: We study the class of Azema-Yor processes defined from a general semimartingale with a continuous running supremum process.
Edit intent: clarity
Original:  Further, we study in detail AY martingales defined from a non-negative local martingale converging to zero at infinity.
Revised:  Secondly we study in detail AY martingales defined from a non-negative local martingale converging to zero at infinity.
Edit intent: coherence
Original:  Finally, we prove new optimal properties of AY martingales relative to concave ordering of terminal laws of martingales .
Revised:  Finally, we characterise Azema-Yor martingales showing they are optimal relative to the concave ordering of terminal laws of martingales .
Edit intent: clarity
Original: We study the class of Azema-Yor processes defined from a general semimartingale with a continuous running supremum process.
Revised: We study the class of Az\'ema-Yor processes defined from a general semimartingale with a continuous running supremum process.
Edit intent: fluency
Original:  We show that they arise as unique strong solutions of the Bachelier stochastic differential equation which we prove is equivalent to the Drawdown equation.
Revised:  We show that they arise as unique strong solutions of the Bachelier stochastic differential equation which we prove is equivalent to the drawdown equation.
Edit intent: fluency
Original:  Solutions of the latter have the drawdown property: they always stay above a given function of their past supremum .
Revised:  Solutions of the latter have the drawdown property: they always stay above a given function of their past maximum .
Edit intent: clarity
Original:  We then show that any process which satisfies the drawdown property is in fact an Azema-Yor process.
Revised:  We then show that any process which satisfies the drawdown property is in fact an Az\'ema-Yor process.
Edit intent: fluency
Original:  The proofs exploit group structure of the set of Azema-Yor processes, indexed by functions, which we introduce.
Revised:  The proofs exploit group structure of the set of Az\'ema-Yor processes, indexed by functions, which we introduce.
Edit intent: fluency
Original:  Secondly we study in detail Azema-Yor martingales defined from a non-negative local martingale converging to zero at infinity.
Revised:  We investigate in detail Az\'ema-Yor martingales defined from a non-negative local martingale converging to zero at infinity.
Edit intent: clarity
Original:  Secondly we study in detail Azema-Yor martingales defined from a non-negative local martingale converging to zero at infinity.
Revised:  Secondly we study in detail Azema-Yor martingales defined from a nonnegative local martingale converging to zero at infinity.
Edit intent: fluency
Original:  We establish relations between Average Value at Risk, Drawdown function, Hardy-Littlewood transform and its generalised inverse.
Revised:  We establish relations between average value at risk, drawdown function, Hardy-Littlewood transform and its generalised inverse.
Edit intent: fluency
Original:  We establish relations between Average Value at Risk, Drawdown function, Hardy-Littlewood transform and its generalised inverse.
Revised:  We establish relations between Average Value at Risk, Drawdown function, Hardy-Littlewood transform and its inverse.
Edit intent: clarity
Original: Lateral inhibition in a gene regulatory network forms a simple double-negative feedback loop , whose pattern-forming behaviour has well been studied in the context of developmental biology.
Revised: Lateral inhibition resulting from a double-negative feedback loop , whose pattern-forming behaviour has well been studied in the context of developmental biology.
Edit intent: clarity
Original:  Time delays in the local and the signalling loops are found to control largely the behaviour of the whole system, such as the time taken for differentiation, and in-phase / out-of-phase inter-cell oscillatory mode relation associated with oscillation death .
Revised:  Time delays in the local and the signalling loops are found to control largely the behaviour of the whole system, such as the time taken for differentiation, and in-phase and out-of-phase inter-cell oscillatory mode relation associated with oscillation death .
Edit intent: fluency
Original:  Very recently, the O(m) bound was improved to O( min m, n^{2.
Revised:  Very recently, the O(m) bound was improved to O( m, n^{2.
Edit intent: clarity
Original: 5\ln n}{d}\}} ) expected time, an expression that is bounded by \~O (n^{1.75}).
Revised: 5\ln n}{d}\}} ) expected time, an expression that is bounded by (n^{1.75}).
Edit intent: clarity
Original:  We then design and analyze a two-stage sampling scheme that reduces the problem of finding a perfect matching in regular bipartite graphs to the same problem on arbitrary bipartite graphs with O(n log n) edges  ) running time, we present a tighter analysis for our special case that results in the stronger }O{d} \}) time mentioned earlier.
Revised:  We then design and analyze a two-stage sampling scheme that reduces the problem of finding a perfect matching in a regular bipartite graph to the same problem on arbitrary bipartite graphs with O(n log n) edges ) running time, we present a tighter analysis for our special case that results in the stronger }O{d} \}) time mentioned earlier.
Edit intent: fluency
Original: A new method of estimating flow characteristics in the Internet is developped in this paper.
Revised: A new method of estimating flow characteristics in the Internet is developed in this paper.
Edit intent: fluency
Original:  By adopting a convenient mouse/elephant dichotomy also %DIFDELCMD < {\em %%% dependent on traffic , it is shown how these variables give a %DIFDELCMD < {\em %%% robust statistical information of long flows . A mathematical framework is developed to estimate the accuracy of the method.
Revised:  By adopting a convenient mouse/elephant dichotomy also %DIFDELCMD < {\em %%% dependent on traffic , it is shown how these variables give a %DIFDELCMD < {\em %%% statistical information of long flows . A mathematical framework is developed to estimate the accuracy of the method.
Edit intent: clarity
Original:  By adopting a convenient mouse/elephant dichotomy also %DIFDELCMD < {\em %%% dependent on traffic , it is shown how these variables give a %DIFDELCMD < {\em %%% robust statistical information of long flows . A mathematical framework is developed to estimate the accuracy of the method.
Revised:  By adopting a convenient mouse/elephant dichotomy also %DIFDELCMD < {\em %%% dependent on traffic , it is shown how these variables give a %DIFDELCMD < {\em %%% robust reliable statistical representation of the number of packets transmitted by large flows during successive time intervals with an appropriate duration . A mathematical framework is developed to estimate the accuracy of the method.
Edit intent: clarity
Original:  The algorithm proposed is tested against experimental data collected from different types of IP traffic .
Revised:  The algorithm proposed is tested against experimental data collected from different types of IP networks .
Edit intent: clarity
Original:  In previous works, we developed analysis techniques that allow studying the applicability of rule sequences, their independence, state reachability and the minimal graph able to fire a sequence.
Revised:  In previous works, we developed analysis techniques enabling the study of the applicability of rule sequences, their independence, state reachability and the minimal graph able to fire a sequence.
Edit intent: clarity
Original:  This matrix (called "nihilation matrix" ) contains the elements that  if present, forbid the application of the rule (i.e. potential dangling edges, or newly added edges, which cannot be already present in the simple digraph).
Revised:  This matrix (called nihilation matrix ) contains the elements that if present, forbid the application of the rule (i.e. potential dangling edges, or newly added edges, which cannot be already present in the simple digraph).
Edit intent: fluency
Original:  This matrix (called "nihilation matrix" ) contains the elements that  if present, forbid the application of the rule (i.e. potential dangling edges, or newly added edges, which cannot be already present in the simple digraph).
Revised:  This matrix (called "nihilation matrix" ) contains the elements that , if present, forbid the application of the rule (i.e. potential dangling edges, or newly added edges, which cannot be already present in the simple digraph).
Edit intent: fluency
Original:  This allows  more flexibility and expressivity than previous approaches, as well as more concise conditions in certain cases.
Revised:  This allows for more flexibility and expressivity than previous approaches, as well as more concise conditions in certain cases.
Edit intent: fluency
Original:  Moreover, all analysis techniques of previous works for the study of sequences can be applied to application conditions.
Revised:  Moreover, all analysis techniques of 21, 22 for the study of sequences can be applied to application conditions.
Edit intent: clarity
Original:  We prove that two large classes of constant-factor approximable problems, namely %DIFDELCMD < \MINF%%% _1 and%DIFDELCMD < \MNP%%% , including the well-known subclass%DIFDELCMD < \MSNP%%% , admit polynomial kernelizations for their natural decision versions.
Revised:  We prove that two large classes of constant-factor approximable problems, namely %DIFDELCMD < \MINF%%% %DIFDELCMD < \MNP%%% , including the well-known subclass%DIFDELCMD < \MSNP%%% , admit polynomial kernelizations for their natural decision versions.
Edit intent: coherence
Original:  We prove that two large classes of constant-factor approximable problems, namely %DIFDELCMD < \MINF%%% _1 and%DIFDELCMD < \MNP%%% , including the well-known subclass%DIFDELCMD < \MSNP%%% , admit polynomial kernelizations for their natural decision versions.
Revised:  We prove that two large classes of constant-factor approximable problems, namely %DIFDELCMD < \MINF%%% _1 and%DIFDELCMD < \MNP%%% %DIFDELCMD < \MSNP%%% , admit polynomial kernelizations for their natural decision versions.
Edit intent: coherence
Original:  This extends results of Cai and Chen (JCSS 1997), stating that the standard parameterizations of problems in %DIFDELCMD < \MSNP %%% and%DIFDELCMD < \MINF%%%  _1 are fixed-parameter tractable, and complements recent research on problems that do not admit polynomial kernelizations (Bodlaender et al.
Revised:  This extends results of Cai and Chen (JCSS 1997), stating that the standard parameterizations of problems in %DIFDELCMD < \MSNP %%% %DIFDELCMD < \MINF%%% _1 are fixed-parameter tractable, and complements recent research on problems that do not admit polynomial kernelizations (Bodlaender et al.
Edit intent: coherence
Original: We study the effects of diffusion in ordering dynamics by considering the Voterand Moran processes in a metapopulation framework, in which individuals are endowed with mobility and diffuse through a spatial structure represented as a graph of patches upon which interactions take place.
Revised: We study the effects of diffusion in Voter/Moran processes by proposing a generalization of ordering dynamics in a metapopulation framework, in which individuals are endowed with mobility and diffuse through a spatial structure represented as a graph of patches upon which interactions take place.
Edit intent: clarity
Original:  We show that diffusion can dramatically affect the time to reach the homogeneous state, independently of the underlying network's topology, while the final consensus emerges through different local/global mechanisms, depending on the mobility strength.
Revised:  We show that diffusion dramatically affects the time to reach the homogeneous state, independently of the underlying network's topology, while the final consensus emerges through different local/global mechanisms, depending on the mobility strength.
Edit intent: clarity
Original:  This is frequently and effectively modeled phenomenologically by a linear filter that extracts the components of the stimulus that are relevant for triggering spikes, and a nonlinear function that relates stimulus to firing probability.
Revised:  This is frequently and effectively modeled phenomenologically by one or more linear filters that extract the components of the stimulus that are relevant for triggering spikes, and a nonlinear function that relates stimulus to firing probability.
Edit intent: clarity
Original: We prove that several variants of the quantum finite automaton (QFA) model are strictly superior to their probabilistic counterparts, in terms of both language recognition power and succinctness, in the one-sided unbounded error setting.
Revised: We prove that several variants of the quantum finite automaton (QFA) model are strictly superior to their probabilistic counterparts, in terms of language recognition power and succinctness, in the one-sided unbounded error setting.
Edit intent: clarity
Original:  We give a characterization of the class of languages recognized by these QFA'swith cutpoint 0 , demonstrating that it is equal to the class of exclusive stochastic languages.
Revised:  We give a characterization of the class of languages recognized by NQFA's , demonstrating that it is equal to the class of exclusive stochastic languages.
Edit intent: clarity
Original: We define a model of games that combines concurrency, imperfect information and stochastic aspects.
Revised: We study a model of games that combines concurrency, imperfect information and stochastic aspects.
Edit intent: clarity
Original:  Those are finite states games in which, at each round, the two players choose, simultaneously andindependently , an action.
Revised:  Those are finite states games in which, at each round, the two players choose, andindependently , an action.
Edit intent: clarity
Original:  Those are finite states games in which, at each round, the two players choose, simultaneously andindependently , an action.
Revised:  Those are finite states games in which, at each round, the two players choose, simultaneously independently , an action.
Edit intent: fluency
Original:  Those are finite states games in which, at each round, the two players choose, simultaneously andindependently , an action.
Revised:  Those are finite states games in which, at each round, the two players choose, simultaneously andsimultaneously and independently , an action.
Edit intent: clarity
Original:  Imperfect information is modelled as follows: both players have an equivalence relation over states and, instead of observing the exact state, they only know to which equivalence class it belongs.
Revised:  Imperfect information is modeled as follows: both players have an equivalence relation over states and, instead of observing the exact state, they only know to which equivalence class it belongs.
Edit intent: fluency
Original:  A play is won by the first player whenever it satisfies the objective.
Edit intent: coherence
Original:  Our main contribution is to prove that the following problem is 2-ExpTime -complete : decide whether the first player has a strategy that ensures her to almost-surely win against any possible strategy of her adversary .
Revised:  Our main contribution is to prove that the following problem is ExpTime -complete : decide whether the first player has a strategy that ensures her to almost-surely win against any possible strategy of her adversary .
Edit intent: clarity
Original:  Our main contribution is to prove that the following problem is 2-ExpTime -complete : decide whether the first player has a strategy that ensures her to almost-surely win against any possible strategy of her adversary .
Revised:  Our main contribution is to prove that the following problem is 2- -complete : decide whether the first player has a strategy that ensures her to almost-surely win against any possible strategy of her adversary .
Edit intent: style
Original:  Our main contribution is to prove that the following problem is 2-ExpTime -complete : decide whether the first player has a strategy that ensures her to almost-surely win against any possible strategy of her adversary .
Revised:  Our main contribution is to prove that the following problem is 2-ExpTime -complete : decide whether the first player has a strategy that ensures her to almost-surely win against any possible strategy of her adversary .
Edit intent: fluency