wanyu/IteraTeR_full_sent huggingface dataset:
Original: We study the asymptotic behaviour of the difference between the Value at Risks VaR(L) and VaR(L+S) for heavy tailed random variables L and S as an application to the sensitivity analysis of quantitative operational risk management in the framework of an advanced measurement approach (AMA) of Basel II . Here the variable L describes the loss amount of the present risk profile and S means the loss amount caused by an additional loss factor.
Revised: We study the asymptotic behaviour of the difference between the Value at Risks VaR(L) and VaR(L+S) for heavy tailed random variables L and S as an application to the sensitivity analysis of quantitative operational risk management in the framework of an advanced measurement approach of Basel II . Here the variable L describes the loss amount of the present risk profile and S means the loss amount caused by an additional loss factor.
Edit intent: clarity
Original: We study the asymptotic behaviour of the difference between the Value at Risks VaR(L) and VaR(L+S) for heavy tailed random variables L and S as an application to the sensitivity analysis of quantitative operational risk management in the framework of an advanced measurement approach (AMA) of Basel II . Here the variable L describes the loss amount of the present risk profile and S means the loss amount caused by an additional loss factor.
Revised: We study the asymptotic behaviour of the difference between the Value at Risks VaR(L) and VaR(L+S) for heavy tailed random variables L and S as an application to the sensitivity analysis of quantitative operational risk management in the framework of an advanced measurement approach (AMA) of Basel II (and III). Here L describes the loss amount of the present risk profile and S means the loss amount caused by an additional loss factor.
Edit intent: meaning-changed
Original: We study the asymptotic behaviour of the difference between the Value at Risks VaR(L) and VaR(L+S) for heavy tailed random variables L and S as an application to the sensitivity analysis of quantitative operational risk management in the framework of an advanced measurement approach (AMA) of Basel II . Here the variable L describes the loss amount of the present risk profile and S means the loss amount caused by an additional loss factor.
Revised: We study the asymptotic behaviour of the difference between the Value at Risks VaR(L) and VaR(L+S) for heavy tailed random variables L and S as an application to the sensitivity analysis of quantitative operational risk management in the framework of an advanced measurement approach (AMA) of Basel II . Here the variable L describes the loss amount of the present risk profile and S describes the loss amount caused by an additional loss factor.
Edit intent: clarity
Original:  We have different types of results according to the magnitude of the relationship of the thicknesses of the tails of L and S. Especially if the tail of S is sufficiently thinner than that of L, then the difference between prior and posterior risk amounts VaR(L+S) - VaR(L) is asymptotically equivalent to the component VaR of S (which is equal to the expected lossof S when L and S are independent) .
Revised:  We obtain different types of results according to the magnitude of the relationship of the thicknesses of the tails of L and S. Especially if the tail of S is sufficiently thinner than that of L, then the difference between prior and posterior risk amounts VaR(L+S) - VaR(L) is asymptotically equivalent to the component VaR of S (which is equal to the expected lossof S when L and S are independent) .
Edit intent: fluency
Original:  We have different types of results according to the magnitude of the relationship of the thicknesses of the tails of L and S. Especially if the tail of S is sufficiently thinner than that of L, then the difference between prior and posterior risk amounts VaR(L+S) - VaR(L) is asymptotically equivalent to the component VaR of S (which is equal to the expected lossof S when L and S are independent) .
Revised:  We have different types of results according to the relative magnitudes of the thicknesses of the tails of L and S. Especially if the tail of S is sufficiently thinner than that of L, then the difference between prior and posterior risk amounts VaR(L+S) - VaR(L) is asymptotically equivalent to the component VaR of S (which is equal to the expected lossof S when L and S are independent) .
Edit intent: clarity
Original:  We have different types of results according to the magnitude of the relationship of the thicknesses of the tails of L and S. Especially if the tail of S is sufficiently thinner than that of L, then the difference between prior and posterior risk amounts VaR(L+S) - VaR(L) is asymptotically equivalent to the component VaR of S (which is equal to the expected lossof S when L and S are independent) .
Revised:  We have different types of results according to the magnitude of the relationship of the thicknesses of the tails of L and S. In particular, if the tail of S is sufficiently thinner than that of L, then the difference between prior and posterior risk amounts VaR(L+S) - VaR(L) is asymptotically equivalent to the component VaR of S (which is equal to the expected lossof S when L and S are independent) .
Edit intent: fluency
Original:  We have different types of results according to the magnitude of the relationship of the thicknesses of the tails of L and S. Especially if the tail of S is sufficiently thinner than that of L, then the difference between prior and posterior risk amounts VaR(L+S) - VaR(L) is asymptotically equivalent to the component VaR of S (which is equal to the expected lossof S when L and S are independent) .
Revised:  We have different types of results according to the magnitude of the relationship of the thicknesses of the tails of L and S. Especially if the tail of S is sufficiently thinner than the tail of L, then the difference between prior and posterior risk amounts VaR(L+S) - VaR(L) is asymptotically equivalent to the component VaR of S (which is equal to the expected lossof S when L and S are independent) .
Edit intent: clarity
Original:  We have different types of results according to the magnitude of the relationship of the thicknesses of the tails of L and S. Especially if the tail of S is sufficiently thinner than that of L, then the difference between prior and posterior risk amounts VaR(L+S) - VaR(L) is asymptotically equivalent to the component VaR of S (which is equal to the expected lossof S when L and S are independent) .
Revised:  We have different types of results according to the magnitude of the relationship of the thicknesses of the tails of L and S. Especially if the tail of S is sufficiently thinner than that of L, then the difference between prior and posterior risk amounts VaR(L+S) - VaR(L) is asymptotically equivalent to the expectation (expected loss) of S .
Edit intent: clarity
Original:  The recursive approach, though not offering an explicit result, needs fewer computations.We further propose a fluid analysis of starvation probability on the file level, given the distribution of file size and the traffic intensity. The starvation probabilities of this paper have many potential applications .
Revised:  The recursive approach, though not offering an explicit result, can obtain the distribution of starvations with non-independent and identically distributed (i.i.d.) arrival process in which an ON/OFF bursty arrival process is considered in this work. We further compute the starvation probability as a function of the amount of prefetched packets for a large number of files via a fluid analysis. Among many potential applications .
Edit intent: meaning-changed
Original:  The starvation probabilities of this paper have many potential applications . We apply them to optimize the  quality of experience (QoE) of media streaming service , by exploiting the tradeoff between the start-up delay and the starvation .
Revised:  The starvation probabilities of this paper have many potential applications of starvation analysis, we show how to apply it to optimize the quality of experience (QoE) of media streaming service , by exploiting the tradeoff between the start-up delay and the starvation .
Edit intent: meaning-changed
Original:  We argue that the mutual information (MI) between a  subset of the inputs X = {X_1, ..., X_n} of  node i and the function f_i(X) associated with node i quantifies the determinative power of this subset of inputs over node i.
Revised:  We argue that the mutual information (MI) between a given subset of the inputs X = {X_1, ..., X_n} of node i and the function f_i(X) associated with node i quantifies the determinative power of this subset of inputs over node i.
Edit intent: clarity
Original:  We argue that the mutual information (MI) between a  subset of the inputs X = {X_1, ..., X_n} of  node i and the function f_i(X) associated with node i quantifies the determinative power of this subset of inputs over node i.
Revised:  We argue that the mutual information (MI) between a subset of the inputs X = {X_1, ..., X_n} of some node i and the function f_i(X) associated with node i quantifies the determinative power of this subset of inputs over node i.
Edit intent: clarity
Original:  We argue that the mutual information (MI) between a  subset of the inputs X = {X_1, ..., X_n} of  node i and the function f_i(X) associated with node i quantifies the determinative power of this subset of inputs over node i.
Revised:  We argue that the mutual information (MI) between a subset of the inputs X = {X_1, ..., X_n} of node i and its associated function f_i(X) associated with node i quantifies the determinative power of this subset of inputs over node i.
Edit intent: clarity
Original:  We argue that the mutual information (MI) between a  subset of the inputs X = {X_1, ..., X_n} of  node i and the function f_i(X) associated with node i quantifies the determinative power of this subset of inputs over node i.
Revised:  We argue that the mutual information (MI) between a subset of the inputs X = {X_1, ..., X_n} of node i and the function f_i(X) quantifies the determinative power of this subset of inputs over node i.
Edit intent: clarity
Original:  We argue that the mutual information (MI) between a  subset of the inputs X = {X_1, ..., X_n} of  node i and the function f_i(X) associated with node i quantifies the determinative power of this subset of inputs over node i.
Revised:  We argue that the mutual information (MI) between a subset of the inputs X = {X_1, ..., X_n} of node i and the function f_i(X) associated with node i quantifies the determinative power of this set of inputs over node i.
Edit intent: clarity
Original:  To study the relation of determinative power to sensitivity to perturbations , we relate the MI to measures of perturbations, such as the influence of a variable, in terms of inequalities. The result shows that, maybe surprisingly, an input that has large influence does not necessarily have large determinative power.
Revised:  To study the relation of determinative power to sensitivity to perturbations to these inputs, and find that, maybe surprisingly, an input that has large influence does not necessarily have large determinative power.
Edit intent: clarity
Original:  As an application of our methods , we analyze the large-scale regulatory network of E. colinumerically: We identify the most determinative nodes and show that a small set of those reduces the overall uncertainty of network states significantly.
Revised:  As an application of our results , we analyze the large-scale regulatory network of E. colinumerically: We identify the most determinative nodes and show that a small set of those reduces the overall uncertainty of network states significantly.
Edit intent: clarity
Original:  As an application of our methods , we analyze the large-scale regulatory network of E. colinumerically: We identify the most determinative nodes and show that a small set of those reduces the overall uncertainty of network states significantly.
Revised:  As an application of our methods , we analyze the large-scale regulatory network of Escherichia coli. We identify the most determinative nodes and show that a small set of those reduces the overall uncertainty of network states significantly.
Edit intent: clarity
Original:  As an application of our methods , we analyze the large-scale regulatory network of E. colinumerically: We identify the most determinative nodes and show that a small set of those reduces the overall uncertainty of network states significantly.
Revised:  As an application of our methods , we analyze the large-scale regulatory network of E. colinumerically: We identify the most determinative nodes and show that a small subset of those reduces the overall uncertainty of network states significantly.
Edit intent: fluency
Original:  As an application of our methods , we analyze the large-scale regulatory network of E. colinumerically: We identify the most determinative nodes and show that a small set of those reduces the overall uncertainty of network states significantly. The network is also found to be tolerant to perturbations of its inputs , which can be seen from the Fourier spectrum of its functions .
Revised:  As an application of our methods , we analyze the large-scale regulatory network of E. colinumerically: We identify the most determinative nodes and show that a small set of those reduces the overall uncertainty of the network state significantly. Furthermore, the network is found to be tolerant to perturbations of its inputs , which can be seen from the Fourier spectrum of its functions .
Edit intent: coherence
Original: The theory of L\'evy models for asset pricing simplifies considerably if one takes a pricing kernel approach, which enables one to bypass market incompleteness issues. The special case of a geometric L\'evy model (GLM) with constant parameters can be regarded as a natural generalisation of the standard geometric Brownian motion model  used in the  Black-Scholes theory .
Revised: The geometric L\'evy model (GLM) with constant parameters can be regarded as a natural generalisation of the standard geometric Brownian motion model used in the Black-Scholes theory .
Edit intent: coherence
Original:  The special case of a geometric L\'evy model (GLM) with constant parameters can be regarded as a natural generalisation of the standard geometric Brownian motion model  used in the  Black-Scholes theory .
Revised:  The special case of a geometric L\'evy model (GLM) with constant parameters can be regarded as a natural generalisation of the geometric Brownian motion model used in the Black-Scholes theory .
Edit intent: clarity
Original:  The special case of a geometric L\'evy model (GLM) with constant parameters can be regarded as a natural generalisation of the standard geometric Brownian motion model  used in the  Black-Scholes theory .
Revised:  The special case of a geometric L\'evy model (GLM) with constant parameters can be regarded as a natural generalisation of the standard geometric Brownian motion model (GBM) used in the Black-Scholes theory .
Edit intent: clarity
Original:  The special case of a geometric L\'evy model (GLM) with constant parameters can be regarded as a natural generalisation of the standard geometric Brownian motion model  used in the  Black-Scholes theory .
Revised:  The special case of a geometric L\'evy model (GLM) with constant parameters can be regarded as a natural generalisation of the standard geometric Brownian motion model used in the derivation of the Black-Scholes theory .
Edit intent: meaning-changed
Original:  The special case of a geometric L\'evy model (GLM) with constant parameters can be regarded as a natural generalisation of the standard geometric Brownian motion model  used in the  Black-Scholes theory .
Revised:  The special case of a geometric L\'evy model (GLM) with constant parameters can be regarded as a natural generalisation of the standard geometric Brownian motion model used in the Black-Scholes formula. The theory of such models simplifies considerably if one takes a pricing kernel approach .
Edit intent: meaning-changed
Original:  In one dimension, once the underlying L\'evy process has been specified, the GLM is characterised by four parameters: the initial asset price, the interest rate, the volatility, and a risk aversionfactor .
Revised:  In one dimension, once the underlying L\'evy process has been specified, the GLM has four parameters: the initial asset price, the interest rate, the volatility, and a risk aversionfactor .
Edit intent: clarity
Original:  In one dimension, once the underlying L\'evy process has been specified, the GLM is characterised by four parameters: the initial asset price, the interest rate, the volatility, and a risk aversionfactor .
Revised:  In one dimension, once the underlying L\'evy process has been specified, the GLM is characterised by four parameters: the initial price, the interest rate, the volatility, and a risk aversionfactor .
Edit intent: clarity
Original:  In one dimension, once the underlying L\'evy process has been specified, the GLM is characterised by four parameters: the initial asset price, the interest rate, the volatility, and a risk aversionfactor .
Revised:  In one dimension, once the underlying L\'evy process has been specified, the GLM is characterised by four parameters: the initial asset price, the interest rate, the volatility, and the risk aversion .
Edit intent: clarity
Original:  The pricing kernel is given by the product of a discount factor and the Esscher martingale associated with the risk aversion parameter. The model is fixed by the requirement that for each asset the product of the asset price and the pricing kernel should be a martingale. In the GBMcase , the risk aversion factor is the so-called market price of risk.
Revised:  The pricing kernel is given by the product of a discount factor and a risk aversion martingale. For GBM , the risk aversion factor is the so-called market price of risk.
Edit intent: clarity
Original:  In the case of foreign exchange, Siegel's paradox implies that it is possible to construct foreign exchange models for which the excess rate of return (above the interest rate differential) is positive both for the exchange rate and the inverse exchange rate.
Revised:  In the case of foreign exchange, Siegel's paradox implies that one can construct foreign exchange models for which the excess rate of return (above the interest rate differential) is positive both for the exchange rate and the inverse exchange rate.
Edit intent: clarity
Original:  In the case of foreign exchange, Siegel's paradox implies that it is possible to construct foreign exchange models for which the excess rate of return (above the interest rate differential) is positive both for the exchange rate and the inverse exchange rate.
Revised:  In the case of foreign exchange, Siegel's paradox implies that it is possible to construct foreign exchange models for which the excess rate of return is positive both for the exchange rate and the inverse exchange rate.
Edit intent: clarity
Original:  We show that in the special but important case of optimal gain cascades (i.e., when all the deactivation rates are identical) the downstream output of an entire cascade can be represented exactly as a single nonlinear module containing an incomplete gamma function with parameters dependent on the input signal as well as the rates and length of the cascade .
Revised:  We show that in the special but important case of optimal-gain cascades (i.e., when all the deactivation rates are identical) the downstream output of an entire cascade can be represented exactly as a single nonlinear module containing an incomplete gamma function with parameters dependent on the input signal as well as the rates and length of the cascade .
Edit intent: fluency
Original:  We show that in the special but important case of optimal gain cascades (i.e., when all the deactivation rates are identical) the downstream output of an entire cascade can be represented exactly as a single nonlinear module containing an incomplete gamma function with parameters dependent on the input signal as well as the rates and length of the cascade .
Revised:  We show that in the special but important case of optimal gain cascades (i.e., when the deactivation rates are identical) the downstream output of an entire cascade can be represented exactly as a single nonlinear module containing an incomplete gamma function with parameters dependent on the input signal as well as the rates and length of the cascade .
Edit intent: clarity
Original:  We show that in the special but important case of optimal gain cascades (i.e., when all the deactivation rates are identical) the downstream output of an entire cascade can be represented exactly as a single nonlinear module containing an incomplete gamma function with parameters dependent on the input signal as well as the rates and length of the cascade .
Revised:  We show that in the special but important case of optimal gain cascades (i.e., when all the deactivation rates are identical) the downstream output of the cascade can be represented exactly as a single nonlinear module containing an incomplete gamma function with parameters dependent on the input signal as well as the rates and length of the cascade .
Edit intent: clarity
Original:  We show that in the special but important case of optimal gain cascades (i.e., when all the deactivation rates are identical) the downstream output of an entire cascade can be represented exactly as a single nonlinear module containing an incomplete gamma function with parameters dependent on the input signal as well as the rates and length of the cascade .
Revised:  We show that in the special but important case of optimal gain cascades (i.e., when all the deactivation rates are identical) the downstream output of an entire cascade can be represented exactly as a lumped nonlinear module containing an incomplete gamma function with parameters dependent on the input signal as well as the rates and length of the cascade .
Edit intent: clarity
Original:  We show that in the special but important case of optimal gain cascades (i.e., when all the deactivation rates are identical) the downstream output of an entire cascade can be represented exactly as a single nonlinear module containing an incomplete gamma function with parameters dependent on the input signal as well as the rates and length of the cascade .
Revised:  We show that in the special but important case of optimal gain cascades (i.e., when all the deactivation rates are identical) the downstream output of an entire cascade can be represented exactly as a single nonlinear module containing an incomplete gamma function with real parameters that depend on the rates and length of the cascade .
Edit intent: clarity