wanyu/IteraTeR_full_sent huggingface dataset:
Original:  We establish a function, r(n), termed athreshold function , such that the probability of the random network being deficiency zero converges to 1 if p_n \ll r(n ){r(n)}}\to \to  and converges to 0 if p_n \gg{r(n)}}\to \to  r(n)  .
Revised:  We establish a function, r(n), termed athreshold function , such that the probability of a random binary network being deficiency zero converges to 1 if p_n \ll r(n ){r(n)}}\to \to and converges to 0 if p_n \gg{r(n)}}\to \to r(n) .
Edit intent: meaning-changed
Original:  We establish a function, r(n), termed athreshold function , such that the probability of the random network being deficiency zero converges to 1 if p_n \ll r(n ){r(n)}}\to \to  and converges to 0 if p_n \gg{r(n)}}\to \to  r(n)  .
Revised:  We establish a function, r(n), termed athreshold function , such that the probability of the random network being deficiency zero converges to 1 if \frac{p_n{r(n)}}\to \to and converges to 0 if p_n \gg{r(n)}}\to \to r(n) .
Edit intent: meaning-changed
Original:  We establish a function, r(n), termed athreshold function , such that the probability of the random network being deficiency zero converges to 1 if p_n \ll r(n ){r(n)}}\to \to  and converges to 0 if p_n \gg{r(n)}}\to \to  r(n)  .
Revised:  We establish a function, r(n), termed athreshold function , such that the probability of the random network being deficiency zero converges to 1 if p_n \ll r(n ){r(n)}}\to 0, as n\to and converges to 0 if p_n \gg{r(n)}}\to \to r(n) .
Edit intent: meaning-changed
Original:  We establish a function, r(n), termed athreshold function , such that the probability of the random network being deficiency zero converges to 1 if p_n \ll r(n ){r(n)}}\to \to  and converges to 0 if p_n \gg{r(n)}}\to \to  r(n)  .
Revised:  We establish a function, r(n), termed athreshold function , such that the probability of the random network being deficiency zero converges to 1 if p_n \ll r(n ){r(n)}}\to \to \infty, and converges to 0 if p_n \gg{r(n)}}\to \to r(n) .
Edit intent: meaning-changed
Original:  We establish a function, r(n), termed athreshold function , such that the probability of the random network being deficiency zero converges to 1 if p_n \ll r(n ){r(n)}}\to \to  and converges to 0 if p_n \gg{r(n)}}\to \to  r(n)  .
Revised:  We establish a function, r(n), termed athreshold function , such that the probability of the random network being deficiency zero converges to 1 if p_n \ll r(n ){r(n)}}\to \to and converges to 0 if \frac{p_n{r(n)}}\to \to r(n) .
Edit intent: meaning-changed
Original:  We establish a function, r(n), termed athreshold function , such that the probability of the random network being deficiency zero converges to 1 if p_n \ll r(n ){r(n)}}\to \to  and converges to 0 if p_n \gg{r(n)}}\to \to  r(n)  .
Revised:  We establish a function, r(n), termed athreshold function , such that the probability of the random network being deficiency zero converges to 1 if p_n \ll r(n ){r(n)}}\to \to and converges to 0 if p_n \gg{r(n)}}\to \infty, as n\to r(n) .
Edit intent: meaning-changed
Original:  We establish a function, r(n), termed athreshold function , such that the probability of the random network being deficiency zero converges to 1 if p_n \ll r(n ){r(n)}}\to \to  and converges to 0 if p_n \gg{r(n)}}\to \to  r(n)  .
Revised:  We establish a function, r(n), termed athreshold function , such that the probability of the random network being deficiency zero converges to 1 if p_n \ll r(n ){r(n)}}\to \to and converges to 0 if p_n \gg{r(n)}}\to \to \infty, where r(n) .
Edit intent: meaning-changed
Original:  We establish a function, r(n), termed athreshold function , such that the probability of the random network being deficiency zero converges to 1 if p_n \ll r(n ){r(n)}}\to \to  and converges to 0 if p_n \gg{r(n)}}\to \to  r(n)  .
Revised:  We establish a function, r(n), termed athreshold function , such that the probability of the random network being deficiency zero converges to 1 if p_n \ll r(n ){r(n)}}\to \to and converges to 0 if p_n \gg{r(n)}}\to \to r(n) =\frac{1 .
Edit intent: meaning-changed
Original:  The first one is , whether we can bisect more than d masses, if we allow for bisections with more general objects such as cones, wedges or double wedges. We answer this question in the affirmative by showing that with all of these objects, we can simultaneously bisect d+1 masses. For double wedges, we prove a stronger statement, namely that d families of d+1 masses each can each by simultaneously bisected by some double wedge such that all double wedges have one hyperplane in common. The second question is, how many masses we can simultaneously equipartition with a k-fan, that is, k half-hyperplanes in R^d, emanating from a common (d-2)-dimensional apex.
Revised:  The first one is how many masses we can simultaneously equipartition with a k-fan, that is, k half-hyperplanes in R^d, emanating from a common (d-2)-dimensional apex.
Edit intent: coherence
Original:  The second question is, how many masses we can simultaneously equipartition with a k-fan, that is, k half-hyperplanes in R^d, emanating from a common (d-2)-dimensional apex.
Revised:  The second question is, how many masses we can simultaneously partition with a k-fan, that is, k half-hyperplanes in R^d, emanating from a common (d-2)-dimensional apex.
Edit intent: fluency
Original:  This question was already studied in the plane, our contribution is to extend the planar results to higher dimensions . All of our results are proved using topological methods. We use some well-established techniques, but also some newer methods. In particular, we introduce a Borsuk-Ulam theorem for flag manifolds, which we believe to be of independent interest .
Revised:  This question was already studied in the plane, but in higher dimensions the only known results are for the case where k is an odd prime. We extend these results to a larger family of values of k. We further present a new result for k=2, which generalizes to cones. The second question considers bisections with double wedges or, equivalently, Ham-Sandwich cuts after projective transformations. Here we prove that given d families of d+1 point sets each, there is always a projective transformation such that after the transformation, each family has a Ham-Sandwich cut. We further prove a result on partitions with parallel hyperplanes after a projective transformation .
Edit intent: meaning-changed
Original:  In this way, various biases can undergo either amplification or attenuation, potentially resulting in enduring preferences and orientations. MEDO is unique in that it specifically models all shaping dynamics in terms of natural selection operating on multiple levels--genetic, neural, and cultural--and even considers aspects of development to themselves be evolutionary processes.
Revised:  In this way, various biases can undergo either amplification or attenuation, resulting in preferences and behavioral orientations of varying degrees of inter-temporal and inter-situational stability. MEDO specifically models all shaping dynamics in terms of natural selection operating on multiple levels--genetic, neural, and cultural--and even considers aspects of development to themselves be evolutionary processes.
Edit intent: clarity
Original:  We limit the cardinality of the signal space to be less than the cardinality of the action space and the state space . This limits the sender's ability of making arbitrarily many action recommendations . We prove the existence of a solution to the sender's utility maximization problem and characterize its properties .
Revised:  We limit the cardinality of the signal space to be less than the cardinality of the action space and the state space , which limits the number of action recommendations that the sender can make. Existence of a maximum to the sender's utility maximization problem and characterize its properties .
Edit intent: clarity
Original:  We prove the existence of a solution to the sender's utility maximization problem and characterize its properties . In solving this problem, we develop a novel approach for solving Bayesian persuasion problems, which can be applied to a wide range of settings. We characterize the sender's willingness to pay for an additional signal as a function of the prior belief, which we interpret as the value of precise communication.
Revised:  We prove the existence of a solution to the sender's problem is proven and its properties are characterized. This generalizes the standard Bayesian Persuasion framework, in which existence results rely on the assumption of rich signal spaces. We analyze the sender's willingness to pay for an additional signal as a function of the prior belief, which we interpret as the value of precise communication.
Edit intent: meaning-changed
Original:  Theory of polymer brushes and models of side-chain-induced internal tension show our data are consistent with a polydisperse aggrecan population, attributable to varying degrees of glycosylation  .
Revised:  We use models of force-extension behavior to show that repulsion between the aggrecans induces an internal tension in the HA chain. Through reference to theories of bottlebrush polymer behavior, we demonstrate that the experimental values of internal tension are consistent with a polydisperse aggrecan population, attributable to varying degrees of glycosylation .
Edit intent: meaning-changed
Original:  Theory of polymer brushes and models of side-chain-induced internal tension show our data are consistent with a polydisperse aggrecan population, attributable to varying degrees of glycosylation  .
Revised:  Theory of polymer brushes and models of side-chain-induced internal tension show our data are consistent with a polydisperse aggrecan population, attributable to varying degrees of glycosylation . By enzymatically deglycosylating aggrecan, we show that aggrecan glycosylation is the structural feature which causes HA stiffening. We then construct a simple stochastic binding model to show that variable glycosylation leads to a wide distribution of internal tensions in HA, causing variations in the mechanics at much longer length-scales .
Edit intent: meaning-changed
Original: Recent conceptual discussion on the nature of the explainability of Artificial Intelligence (AI) has largely been limited to data-driven investigations. This paper identifies some shortcomings of this approach to help strengthen the debate on this subject. Building on recent philosophical work on the nature of explanations, I demonstrate the significance of two non-data driven, non-causal explanatory elements: (1) mathematical structures that are the grounds for capturing the decision-making situation;
Revised: The social implications of algorithmic decision-making situation;
Edit intent: coherence
Original:  Building on recent philosophical work on the nature of explanations, I demonstrate the significance of two non-data driven, non-causal explanatory elements: (1) mathematical structures that are the grounds for capturing the decision-making situation; (2) statistical and optimality facts in terms of which the algorithm is designed and implemented. I argue that these elements feature directly in important aspects of AI explainability. I then propose a hierarchical framework that acknowledges the existence of various types of explanation, each of which reveals an aspect of explanation, and answers to a different kind of why-question. The usefulness of this framework will be illustrated by bringing it to bear on some salient normative concerns about the use of AI decision-making systems in society .
Revised:  Building on recent philosophical work on the nature of explanations, I demonstrate the significance of two non-data driven, non-causal explanatory elements: (1) mathematical structures that are the grounds for capturing the decision-making in sensitive contexts have generated lively debates among multiple stakeholders, such as moral and political philosophers, computer scientists, and the public. Yet, the lack of a common language and a conceptual framework for an appropriate bridging of the moral, technical, and political aspects of the debate prevents the discussion to be as effective as it can be. Social scientists and psychologists are contributing to this debate by gathering a wealth of empirical data, yet a philosophical analysis of the social implications of algorithmic decision-making systems in society .
Edit intent: meaning-changed
Original:  The usefulness of this framework will be illustrated by bringing it to bear on some salient normative concerns about the use of AI decision-making systems in society .
Revised:  The usefulness of this framework will be illustrated by bringing it to bear on some salient normative concerns about the use of AI decision-making remains comparatively impoverished. In attempting to address this lacuna, this paper argues that a hierarchy of different types of explanations for why and how an algorithmic decision outcome is achieved can establish the relevant connection between the moral and technical aspects of algorithmic decision-making. In particular, I offer a multi-faceted conceptual framework for the explanations and the interpretations of algorithmic decisions, and I claim that this framework can lay the groundwork for a focused discussion among multiple stakeholders about the social implications of algorithmic decision-making, as well as AI governance and ethics more generally .
Edit intent: meaning-changed
Original:  We  characterize the unique equilibrium value function of the sender given any disclosure rule.
Revised:  We focus on truth-leaning equilibria, where the sender discloses truthfully when doing so is optimal, and the receiver does not discount off-path messages. We show that, given any disclosure rule, all equilibria are payoff equivalent and characterize the unique equilibrium value function of the sender given any disclosure rule.
Edit intent: meaning-changed
Original:  We  characterize the unique equilibrium value function of the sender given any disclosure rule. Applying this characterization , we study left-censored disclosure, where evidence is a sequence of signals, and the sender can truncate evidence from the left.
Revised:  We characterize the unique equilibrium value function of the sender . We also propose a method to construct equilibria for a broad class of games. Applying these results , we study left-censored disclosure, where evidence is a sequence of signals, and the sender can truncate evidence from the left.
Edit intent: meaning-changed
Original:  In equilibrium, seemingly sub-optimal messages are disclosed, and the sender's disclosure contains the longest truncation that yields the maximal difference between the number of favorable and unfavorable signals . These findings are results of coordination among senders with different evidence endowment .
Revised:  In equilibrium, seemingly sub-optimal messages are disclosed, and the sender's disclosure contains the longest truncation that yields the maximal difference between the number of favorable and unfavorable signals .
Edit intent: clarity
Original:  We focus on truth-leaning equilibria  , where the sender discloses truthfully when doing so is optimal, and the receiver does not discount off-path messages. We show that, given any disclosure rule, all equilibria are payoff equivalent and characterize the unique equilibrium valuefunction of the sender. We also propose a method to construct equilibria for a broad class of games. Applying these results, we study left-censored disclosure, where evidence is a sequence of signals, and the sender can truncate evidence from the left.
Revised:  We focus on truth-leaning equilibria , where the sender discloses truthfully when doing so is optimal, and the receiver does not discount off-path disclosure at face value.
Edit intent: clarity
Original:  In equilibrium, seemingly sub-optimal messages are disclosed, and the sender's disclosure contains the longest truncation that yields the maximal difference between the number of favorable and unfavorable signals .
Revised:  In equilibrium, seemingly sub-optimal messages are disclosed, and the sender's disclosure contains the longest truncation that yields the maximal difference between the number of good and bad signals. We also study a general framework of disclosure games which is compatible with large evidence spaces, a wide range of disclosure technologies, and finitely many states. We characterize the unique equilibrium value function of the sender and propose a method to construct equilibria for a broad class of games .
Edit intent: meaning-changed
Original:  We show that cell-to-cell molecule exchange induces a collective two-cell critical point . We find a slow-down of critical dynamics, reflected in the dynamic exponent z increasing from its well-mixed value (z = 2) to a two-cell collective state (z > 2). Finally, we show that the mutual information between the cells peaks at this critical point , and can remain large far from the critical point if the cells assume the roles of producer/consumer .
Revised:  We show that cell-to-cell molecule exchange induces a collective two-cell critical point and that the mutual information between the cells peaks at this critical point , and can remain large far from the critical point if the cells assume the roles of producer/consumer .
Edit intent: coherence
Original:  Finally, we show that the mutual information between the cells peaks at this critical point , and can remain large far from the critical point if the cells assume the roles of producer/consumer .
Revised:  Finally, we show that the mutual information between the cells peaks at this critical point , and can remain large far from the critical point on a manifold of cellular states, but scales logarithmically with the correlation time of the system, resulting in an information-correlation time tradeoff. This tradeoff is strictly imposed, suggesting the correlation time as a proxy for the mutual information .
Edit intent: meaning-changed
Original: The global minimum-variance portfolio is a typical choice for investors because of its simplicity and broad applicability. Although it requires only one input, namely the covariance matrix of asset returns, estimating the optimal solution remains a challenge.
Revised: The global minimum-variance portfolio over the Markowitz portfolio as this allows the estimation risk to be confined to the covariance matrix of asset returns, estimating the optimal solution remains a challenge.
Edit intent: meaning-changed
Original:  Although it requires only one input, namely the covariance matrix of asset returns, estimating the optimal solution remains a challenge. In the presence of high-dimensionality in the data, the sample estimator becomes ill-conditioned , which negates the positive effect of diversification in an out-of-sample setting .
Revised:  Although it requires only one input, namely the covariance matrix of returns. For high-dimensional data, however, it is well-known that the sample covariance matrix is ill-conditioned , which negates the positive effect of diversification in an out-of-sample setting .
Edit intent: clarity
Original:  To address this issue, we review recent covariance matrix estimators and extend the literature by suggesting a multi-fold cross-validation technique . In detail, conducting an extensive empirical analysis with four datasets based on the S\&P 500, we evaluate how the data-driven choice of specific tuning parameters within the proposed cross-validation approach affects the out-of-sample performance of the global minimum-variance portfolio .
Revised:  To address this issue, we review recent covariance matrix estimators and extend the literature by suggesting a multi-fold cross-validation technique for selecting the necessary tuning parameters within each method. Conducting an extensive empirical analysis with four datasets based on the S\&P 500, we evaluate how the data-driven choice of specific tuning parameters within the proposed cross-validation approach affects the out-of-sample performance of the global minimum-variance portfolio .
Edit intent: meaning-changed
Original:  In detail, conducting an extensive empirical analysis with four datasets based on the S\&P 500, we evaluate how the data-driven choice of specific tuning parameters within the proposed cross-validation approach affects the out-of-sample performance of the global minimum-variance portfolio .
Revised:  In detail, conducting an extensive empirical analysis , we show how the data-driven choice of specific tuning parameters within the proposed cross-validation approach affects the out-of-sample performance of the global minimum-variance portfolio .
Edit intent: clarity
Original:  In detail, conducting an extensive empirical analysis with four datasets based on the S\&P 500, we evaluate how the data-driven choice of specific tuning parameters within the proposed cross-validation approach affects the out-of-sample performance of the global minimum-variance portfolio .
Revised:  In detail, conducting an extensive empirical analysis with four datasets based on the S\&P 500, we evaluate how the data-driven choice of specific tuning parameters with the proposed cross-validation approach affects the out-of-sample performance of the global minimum-variance portfolio .
Edit intent: clarity
Original:  In detail, conducting an extensive empirical analysis with four datasets based on the S\&P 500, we evaluate how the data-driven choice of specific tuning parameters within the proposed cross-validation approach affects the out-of-sample performance of the global minimum-variance portfolio .
Revised:  In detail, conducting an extensive empirical analysis with four datasets based on the S\&P 500, we evaluate how the data-driven choice of specific tuning parameters within the proposed cross-validation improves the out-of-sample performance of the global minimum-variance portfolio .
Edit intent: clarity
Original:  In detail, conducting an extensive empirical analysis with four datasets based on the S\&P 500, we evaluate how the data-driven choice of specific tuning parameters within the proposed cross-validation approach affects the out-of-sample performance of the global minimum-variance portfolio . In particular, for cases in which the efficiency of a covariance estimator is strongly influenced by the choice of a tuning parameter, we detect a clear relationship between the optimality criterion for its selection within the cross-validation and the evaluated performance measure. Finally, we show that using cross-validation can improve the performance of highly efficient estimators even when the data-driven covariance parameter deviates from its theoretically optimal value .
Revised:  In detail, conducting an extensive empirical analysis with four datasets based on the S\&P 500, we evaluate how the data-driven choice of specific tuning parameters within the proposed cross-validation approach affects the out-of-sample performance of the global minimum-variance portfolio .
Edit intent: coherence
Original: Investors often prefer the global minimum-variance portfolio over the Markowitz portfolio as this allows the estimation risk to be confined to the covariance matrix of returns. For high-dimensional data, however, it is well-known that the sample covariance matrix is ill-conditioned and leads to suboptimal portfolios  .
Revised: Investors often prefer the global minimum-variance portfolio over the Markowitz portfolio as this allows the estimation risk to be confined to the covariance matrix of asset returns, estimating the optimal solution remains a challenge. In the presence of high-dimensionality in the data, the sample covariance matrix is ill-conditioned and leads to suboptimal portfolios .
Edit intent: meaning-changed