wanyu/IteraTeR_full_sent huggingface dataset:
Original:  As we will explicitly demonstrate, the periodicity solution concept has implications for non-trivial realistic games, which renders this solution concept very valuable. The most striking application of periodicity is that in mixed strategy strategic form games, we were able to find solutions that result to values for the utility function of each player , that are equal to the Nash equilibrium ones , with the difference that in the Nash strategiesplaying, the payoffs strongly depend on what the opponent plays, while in the periodic strategies case, the payoffs of each player are completely robust against what the opponent plays.
Revised:  As we will explicitly demonstrate, the periodicity solution concept has implications for non-trivial games. In mixed strategy strategic form games, we were able to find solutions that result to values for the utility function of each player , that are equal to the Nash equilibrium ones , with the difference that in the Nash strategiesplaying, the payoffs strongly depend on what the opponent plays, while in the periodic strategies case, the payoffs of each player are completely robust against what the opponent plays.
Edit intent: clarity
Original:  The most striking application of periodicity is that in mixed strategy strategic form games, we were able to find solutions that result to values for the utility function of each player , that are equal to the Nash equilibrium ones , with the difference that in the Nash strategiesplaying, the payoffs strongly depend on what the opponent plays, while in the periodic strategies case, the payoffs of each player are completely robust against what the opponent plays.
Revised:  The most striking application of periodicity is that in mixed strategy strategic form games, periodic solutions yield values for the utility function of each player , that are equal to the Nash equilibrium ones , with the difference that in the Nash strategiesplaying, the payoffs strongly depend on what the opponent plays, while in the periodic strategies case, the payoffs of each player are completely robust against what the opponent plays.
Edit intent: clarity
Original:  The most striking application of periodicity is that in mixed strategy strategic form games, we were able to find solutions that result to values for the utility function of each player , that are equal to the Nash equilibrium ones , with the difference that in the Nash strategiesplaying, the payoffs strongly depend on what the opponent plays, while in the periodic strategies case, the payoffs of each player are completely robust against what the opponent plays.
Revised:  The most striking application of periodicity is that in mixed strategy strategic form games, we were able to find solutions that result to values for the utility function of each player that are equal to the Nash equilibrium ones , with the difference that in the Nash strategiesplaying, the payoffs strongly depend on what the opponent plays, while in the periodic strategies case, the payoffs of each player are completely robust against what the opponent plays.
Edit intent: fluency
Original:  The most striking application of periodicity is that in mixed strategy strategic form games, we were able to find solutions that result to values for the utility function of each player , that are equal to the Nash equilibrium ones , with the difference that in the Nash strategiesplaying, the payoffs strongly depend on what the opponent plays, while in the periodic strategies case, the payoffs of each player are completely robust against what the opponent plays.
Revised:  The most striking application of periodicity is that in mixed strategy strategic form games, we were able to find solutions that result to values for the utility function of each player , that are equal to the Nash equilibrium ones . In contrast to the Nash strategies, here the payoffs of each player are completely robust against what the opponent plays.
Edit intent: coherence
Original:  The most striking application of periodicity is that in mixed strategy strategic form games, we were able to find solutions that result to values for the utility function of each player , that are equal to the Nash equilibrium ones , with the difference that in the Nash strategiesplaying, the payoffs strongly depend on what the opponent plays, while in the periodic strategies case, the payoffs of each player are completely robust against what the opponent plays.
Revised:  The most striking application of periodicity is that in mixed strategy strategic form games, we were able to find solutions that result to values for the utility function of each player , that are equal to the Nash equilibrium ones , with the difference that in the Nash strategiesplaying, the payoffs strongly depend on what the opponent plays, while in the periodic strategies case, the payoffs of each player are robust against what the opponent plays.
Edit intent: clarity
Original:   We formally define and study periodic strategies in two player perfect information strategic form games , with pure strategies and generalize the results to include multiplayer games with perfect information.
Revised:  Sometimes, periodicity strategies yield higher utilities, and sometimes the Nash strategies do, but often the utilities of these two strategies coincide. We formally define and study periodic strategies in two player perfect information strategic form games , with pure strategies and generalize the results to include multiplayer games with perfect information.
Edit intent: meaning-changed
Original:   We formally define and study periodic strategies in two player perfect information strategic form games , with pure strategies and generalize the results to include multiplayer games with perfect information. We prove that every non-trivial finite game has at least one periodic strategy, with non-trivial meaning a game with non-degenerate payoffs.
Revised:  We formally define and study periodic strategies in two player perfect information strategic form games , with pure strategies and we prove that every non-trivial finite game has at least one periodic strategy, with non-trivial meaning a game with non-degenerate payoffs.
Edit intent: coherence
Original:  In principle the algorithm we provide, holds true for every non-trivial game, because in degenerate games, inconsistencies can occur. In addition, we also address the incomplete information games in the context of Bayesian games, in which case generalizations of Bernheim's rationalizability offers us the possibility to embed the periodicity concept in the Bayesian games framework. Applying the algorithm of periodic strategies in the case where mixed strategies are used, we find some very interesting outcomes with useful quantitative features for some classes of games .
Revised:  In some classes of games where mixed strategies are used, we identify quantitative features. Particularly interesting are the implications for collective action games, since there the collective action strategy can be incorporated in a purely non-cooperative context. Moreover, we address the periodicity issue when the players have a continuum set of strategies available .
Edit intent: clarity
Original:  Our motivation is to understand the large macro-economic fluctuations observed in the "Mark I" ABM devised by D. Delli Gatti and collaborators. Our major finding is the  existence of a first order (discontinuous) phase transition between a "good economy" where unemployment is low, and a "bad economy" where unemployment is high.
Revised:  Our motivation is to understand the large macro-economic fluctuations observed in the "Mark I" ABM . Our central finding is the existence of a first order (discontinuous) phase transition between a "good economy" where unemployment is low, and a "bad economy" where unemployment is high.
Edit intent: clarity
Original:  One is to allow this hiring/firing propensity to depend on the financial fragility of firms .
Revised:  One is to introduce a bankruptcy threshold, limiting the leverage of firms. This leads to a rich phase diagram with, in particular, a region where acute endogenous crises occur, during which the unemployment rate shoots up before the economy can recover. We allow the hiring/firing propensity to depend on the financial fragility of firms .
Edit intent: meaning-changed
Original:  One is to allow this hiring/firing propensity to depend on the financial fragility of firms . Quite interestingly, we find that in this case, the above transition survives but becomes second order. We also studied simple wage policies and confidence feedback effects, whereby higher unemployment increases the saving propensity of households. We observe several interesting effects, such as the appearance of acute endogenous crises, during which the unemployment rate shoots up before the economy recovers .
Revised:  One is to allow this hiring/firing propensity to depend on the financial fragility of firms , and introduce simple wage update policies. This leads to inflation (in the "good" phase) or deflation (in the "bad" phase), but leaves the overall phase diagram of the model essentially unchanged. We have finally explored the effect of simple monetary policies that attempt to contain rising unemployment and defang crises .
Edit intent: meaning-changed
Original: Living cells can sense their environment with high precision. Yet, the resources required for sensing with high precision is an open question. Here we address this question for both equilibrium and non-equilibrium systems. We find that in equilibrium systems the precision of sensing is fundamentally limited by the number of receptors;
Revised: Living cells deploy many resources to sense their environments, including receptors, downstream signaling molecules, time and fuel. However, it is not known which resources fundamentally limit the precision of sensing, like weak links in a chain, and which can compensate each other, leading to trade-offs between them. We show by modeling that in equilibrium systems the precision of sensing is fundamentally limited by the number of receptors;
Edit intent: meaning-changed
Original:  the signaling network that transmits the information from the receptors to the interior of the cell can never increase the precisionof sensing. We show that this limit arises from a fundamental trade-off between the removal of the extrinsic noise in the receptor state and the suppression of the intrinsic noise in the signaling network.
Revised:  the signaling network that transmits the information from the receptors to the interior of the cell can never increase precision. This limit arises from a fundamental trade-off between the removal of the extrinsic noise in the receptor state and the suppression of the intrinsic noise in the signaling network.
Edit intent: clarity
Original:  We show that this limit arises from a fundamental trade-off between the removal of the extrinsic noise in the receptor state and the suppression of the intrinsic noise in the signaling network. We next prove that only non-equilibrium systems can lift this trade-off : They can integrate the receptor state over time while suppressing the intrinsic noise by using energy to store the receptor state into stable modification states of the readout molecules.
Revised:  We show that this limit arises from a fundamental trade-off between the removal of the extrinsic noise in the receptor state and the suppression of the intrinsic noise in the downstream network. Non-equilibrium systems can lift this trade-off : They can integrate the receptor state over time while suppressing the intrinsic noise by using energy to store the receptor state into stable modification states of the readout molecules.
Edit intent: clarity
Original:  We next prove that only non-equilibrium systems can lift this trade-off : They can integrate the receptor state over time while suppressing the intrinsic noise by using energy to store the receptor state into stable modification states of the readout molecules.
Revised:  We next prove that only non-equilibrium systems can lift this trade-off by storing the receptor state over time while suppressing the intrinsic noise by using energy to store the receptor state into stable modification states of the readout molecules.
Edit intent: clarity
Original:  We next prove that only non-equilibrium systems can lift this trade-off : They can integrate the receptor state over time while suppressing the intrinsic noise by using energy to store the receptor state into stable modification states of the readout molecules. We explicitly calculate the resources required for a canonical signaling motif, a push-pull network .
Revised:  We next prove that only non-equilibrium systems can lift this trade-off : They can integrate the receptor state over time while suppressing the intrinsic noise by using energy to store the receptor state into stable modification states of downstream molecules. As we quantify for a push-pull network .
Edit intent: coherence
Original:  We explicitly calculate the resources required for a canonical signaling motif, a push-pull network . We arrive at an analytical expression that shows that storing the state of the bound receptor over time requires at least one readout molecule to store the state and at least 4 kT of energy to store it reliably. Thus, each of the resources -- time, protein copy numbers, and energy -- limits sensing, and it is the limiting resource which places the fundamental limit on sensing .
Revised:  We explicitly calculate the resources required for a canonical signaling motif, a push-pull network , this requires i) time and receptors; ii) downstream molecules; iii) energy (fuel turnover) to drive modification. These three resource classes cannot compensate each other, and it is the limiting resource which places the fundamental limit on sensing .
Edit intent: clarity
Original:  Thus, each of the resources -- time, protein copy numbers, and energy -- limits sensing, and it is the limiting resource which places the fundamental limit on sensing .
Revised:  Thus, each of the resources -- time, protein copy numbers, and energy -- limits sensing, and it is the limiting class which sets the fundamental sensing limit. Within each class, trade-offs are possible. Energy allows a power-speed trade-off, while time can be traded against receptors .
Edit intent: meaning-changed
Original: We propose a modified algorithm - Multifractal Cross-Correlation Analysis (MFCCA) - that  is able to consistently identify and quantify  multifractal cross-correlations between two time series.
Revised: We propose a novel algorithm - Multifractal Cross-Correlation Analysis (MFCCA) - that is able to consistently identify and quantify multifractal cross-correlations between two time series.
Edit intent: clarity
Original: We propose a modified algorithm - Multifractal Cross-Correlation Analysis (MFCCA) - that  is able to consistently identify and quantify  multifractal cross-correlations between two time series.
Revised: We propose a modified algorithm - Multifractal Cross-Correlation Analysis (MFCCA) - that constitutes a consistent extension of the Detrended Cross-Correlation Analysis (DCCA) and is able to consistently identify and quantify multifractal cross-correlations between two time series.
Edit intent: meaning-changed
Original: We propose a modified algorithm - Multifractal Cross-Correlation Analysis (MFCCA) - that  is able to consistently identify and quantify  multifractal cross-correlations between two time series.
Revised: We propose a modified algorithm - Multifractal Cross-Correlation Analysis (MFCCA) - that is able to properly identify and quantify multifractal cross-correlations between two time series.
Edit intent: clarity
Original: We propose a modified algorithm - Multifractal Cross-Correlation Analysis (MFCCA) - that  is able to consistently identify and quantify  multifractal cross-correlations between two time series.
Revised: We propose a modified algorithm - Multifractal Cross-Correlation Analysis (MFCCA) - that is able to consistently identify and quantify subtle characteristics of multifractal cross-correlations between two time series.
Edit intent: meaning-changed
Original:  The principal component of the related improvement is proper incorporation of the sign of fluctuations . We present a broad analysis of the model fractal stochastic processes as well as of the real-world signals and show that MFCCA is a robust tool and allows a reliable quantification of the cross-correlative structure of analyzed processes.
Revised:  The principal component of the related improvement is proper incorporation of the sign of fluctuations to their generalized moments. Furthermore, we present a broad analysis of the model fractal stochastic processes as well as of the real-world signals and show that MFCCA is a robust tool and allows a reliable quantification of the cross-correlative structure of analyzed processes.
Edit intent: meaning-changed
Original:  We present a broad analysis of the model fractal stochastic processes as well as of the real-world signals and show that MFCCA is a robust tool and allows a reliable quantification of the cross-correlative structure of analyzed processes.
Revised:  We present a broad analysis of the model fractal stochastic processes as well as of the real-world signals and show that MFCCA is a robust and selective tool at the same time, and therefore allows for a reliable quantification of the cross-correlative structure of analyzed processes.
Edit intent: meaning-changed
Original:  This relation provides information about the character of potential multifractality in cross-correlations of the processes under study and thus enables selective insight into their dynamics . Using also an example of financial time series from the stock market we show that waiting times and price increments of the companies are multifractally cross-correlated but only for relatively large fluctuations, whereas the small ones could be considered mutually independent .
Revised:  This relation provides information about character of potential multifractality in cross-correlations of the processes under study and thus enables selective insight into their dynamics . Using also an example of financial time series from the stock market we show that waiting times and price increments of the companies are multifractally cross-correlated but only for relatively large fluctuations, whereas the small ones could be considered mutually independent .
Edit intent: fluency
Original:  This relation provides information about the character of potential multifractality in cross-correlations of the processes under study and thus enables selective insight into their dynamics . Using also an example of financial time series from the stock market we show that waiting times and price increments of the companies are multifractally cross-correlated but only for relatively large fluctuations, whereas the small ones could be considered mutually independent .
Revised:  This relation provides information about the character of potential multifractality in cross-correlations and thus enables selective insight into their dynamics . Using also an example of financial time series from the stock market we show that waiting times and price increments of the companies are multifractally cross-correlated but only for relatively large fluctuations, whereas the small ones could be considered mutually independent .
Edit intent: clarity
Original:  This relation provides information about the character of potential multifractality in cross-correlations of the processes under study and thus enables selective insight into their dynamics . Using also an example of financial time series from the stock market we show that waiting times and price increments of the companies are multifractally cross-correlated but only for relatively large fluctuations, whereas the small ones could be considered mutually independent .
Revised:  This relation provides information about the character of potential multifractality in cross-correlations of the processes under study and thus enables a deeper insight into dynamics of the analyzed processes than allowed by any other related method available so far. By using examples of time series from the stock market we show that waiting times and price increments of the companies are multifractally cross-correlated but only for relatively large fluctuations, whereas the small ones could be considered mutually independent .
Edit intent: clarity
Original:  This relation provides information about the character of potential multifractality in cross-correlations of the processes under study and thus enables selective insight into their dynamics . Using also an example of financial time series from the stock market we show that waiting times and price increments of the companies are multifractally cross-correlated but only for relatively large fluctuations, whereas the small ones could be considered mutually independent .
Revised:  This relation provides information about the character of potential multifractality in cross-correlations of the processes under study and thus enables selective insight into their dynamics . Using also an example of financial time series from stock market, we show that waiting times and price increments of the companies are multifractally cross-correlated but only for relatively large fluctuations, whereas the small ones could be considered mutually independent .
Edit intent: fluency
Original:  This relation provides information about the character of potential multifractality in cross-correlations of the processes under study and thus enables selective insight into their dynamics . Using also an example of financial time series from the stock market we show that waiting times and price increments of the companies are multifractally cross-correlated but only for relatively large fluctuations, whereas the small ones could be considered mutually independent .
Revised:  This relation provides information about the character of potential multifractality in cross-correlations of the processes under study and thus enables selective insight into their dynamics . Using also an example of financial time series from the stock market we show that financial fluctuations typically cross-correlate multifractally only for relatively large fluctuations, whereas the small ones could be considered mutually independent .
Edit intent: clarity
Original:  This relation provides information about the character of potential multifractality in cross-correlations of the processes under study and thus enables selective insight into their dynamics . Using also an example of financial time series from the stock market we show that waiting times and price increments of the companies are multifractally cross-correlated but only for relatively large fluctuations, whereas the small ones could be considered mutually independent .
Revised:  This relation provides information about the character of potential multifractality in cross-correlations of the processes under study and thus enables selective insight into their dynamics . Using also an example of financial time series from the stock market we show that waiting times and price increments of the companies are multifractally cross-correlated but only for relatively large fluctuations, whereas small fluctuations remain mutually independent even at maximum of such cross-correlations. Finally, we indicate possible utility of MFCCA to study effects of the time-lagged cross-correlations .
Edit intent: meaning-changed
Original:  The ] basic risky asset price model  we construct here is  drift uncertain and volatility uncertain , we describe such model by using general G-Brownian motion and call it as G-asset price system.
Revised:  We use the nonlinear analysis tool, i.e., G-frame work ] basic risky asset price model we construct here is drift uncertain and volatility uncertain , we describe such model by using general G-Brownian motion and call it as G-asset price system.
Edit intent: meaning-changed