wanyu/IteraTeR_full_sent huggingface dataset:
Original:  and (ii) chain-like, associated with high-volatility economic crisis . When we examined successive corresponding segments within the present housing bubble financial crisis, we find that each MST can be obtained from the one before it through a minimal set of primitive rearrangements, each representing a statistically significant change in the cross correlations of the sectors involved .
Revised:  and (ii) chain-like, associated with high-volatility economic crisis .
Edit intent: coherence
Original:   Analyzed performance metrics include the average secondary user throughput and the average collision probability between the primary and secondary users.
Revised:  The analytical framework models the following: number of sensing stages, physical layer sensing techniques, single and parallel channel access, primary and secondary user traffic, as well as buffering of incoming secondary user traffic. Analyzed performance metrics include the average secondary user throughput and the average collision probability between the primary and secondary users.
Edit intent: meaning-changed
Original:  The analysis framework takes into account buffering of incoming secondary user traffic, parallel and single channel access, as well as prolonged channel observation periods at the first and last stage of sensing. The main results show that when a constraint is given upon the probability of primary user mis-detection , multi-stage sensing is in most cases superior to the single stage sensing counterpart.
Revised:  Our results show that when a constraint is given upon the probability of primary user mis-detection , multi-stage sensing is in most cases superior to the single stage sensing counterpart.
Edit intent: clarity
Original: We present an analytical framework which enables performance evaluation of different multi-channel multi-stage spectrum sensing algorithms for Opportunistic Spectrum Access networks.
Revised: Multi-stage sensing is a novel concept that refers to a general class of spectrum sensing algorithms that divide the sensing process into a number of sequential stages. The number of sensing stages and the sensing technique per stage can be used to optimize performance with respect to secondary user throughput and the collision probability between primary and secondary users. So far, the impact of multi-stage sensing on network throughput and collision probability for a realistic network model is relatively unexplored. Therefore, we present the first analytical framework which enables performance evaluation of different multi-channel multi-stage spectrum sensing algorithms for Opportunistic Spectrum Access networks.
Edit intent: meaning-changed
Original:  The analytical framework models the following : number of sensing stages, physical layer sensing techniques  , single and parallel channel access, primary and secondary user traffic, as well as buffering of incoming secondary user traffic  .
Revised:  The contribution of our work lies in studying the effect of the following parameters on performance : number of sensing stages, physical layer sensing techniques , single and parallel channel access, primary and secondary user traffic, as well as buffering of incoming secondary user traffic .
Edit intent: clarity
Original:  The analytical framework models the following : number of sensing stages, physical layer sensing techniques  , single and parallel channel access, primary and secondary user traffic, as well as buffering of incoming secondary user traffic  .
Revised:  The analytical framework models the following : number of sensing stages, physical layer sensing techniques and durations per each stage , single and parallel channel access, primary and secondary user traffic, as well as buffering of incoming secondary user traffic .
Edit intent: meaning-changed
Original:  The analytical framework models the following : number of sensing stages, physical layer sensing techniques  , single and parallel channel access, primary and secondary user traffic, as well as buffering of incoming secondary user traffic  .
Revised:  The analytical framework models the following : number of sensing stages, physical layer sensing techniques , single and parallel channel sensing and access, number of available channels, primary and secondary user traffic, as well as buffering of incoming secondary user traffic .
Edit intent: meaning-changed
Original:  The analytical framework models the following : number of sensing stages, physical layer sensing techniques  , single and parallel channel access, primary and secondary user traffic, as well as buffering of incoming secondary user traffic  .
Revised:  The analytical framework models the following : number of sensing stages, physical layer sensing techniques , single and parallel channel access, primary and secondary user traffic, as well as buffering of incoming secondary user traffic , as well as MAC layer sensing algorithms .
Edit intent: meaning-changed
Original:  Closed-form solution for these options first appeared in Longstaff (1990) for the case when  underlying asset follows a geometric Brownian motion with the constant interest rate and volatility. Unfortunately there are several typographical errors in the published formula for the holder-extendible put. These are subsequently repeated in textbooks, other papers and software. This short paperpresents a correct formula. Also, to generalize, the option price is derived for the case of  a geometric Brownian motion with the time-dependent drift and volatility  .
Revised:  Closed-form solution for these options first appeared in Longstaff (1990) for the case when underlying asset follows a geometric Brownian motion with the constant interest rate , volatility, and non-negative "dividend" yield. In this paper, the option price is derived for the case of a geometric Brownian motion with the time-dependent drift and volatility .
Edit intent: clarity
Original:  Also, to generalize, the option price is derived for the case of  a geometric Brownian motion with the time-dependent drift and volatility  .
Revised:  Also, to generalize, the option price is derived for the case of a geometric Brownian motion with the time-dependent drift and volatility which is important to use the solutions in real life applications. The formulas are derived for the drift that may include non-negative or negative "dividend" yield. The latter case results in a new solution type that has not been studied in the literature. Several typographical errors in the formula for the holder-extendible put, typically repeated in textbooks and software, are corrected .
Edit intent: meaning-changed
Original:  This gives as a result an integro-differential equation, which can be solved analytically in some cases and numerically in others.
Revised:  This technique gives a dynamical insight into the evolution of the PDF, e.g., allowing the calculation of its relaxation times. Their equilibrium PDFs can also be calculated by finding its stationary solutions. This gives as a result an integro-differential equation, which can be solved analytically in some cases and numerically in others.
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Original: In a continuous-path semimartingale market model , we perform an initial enlargement of the filtration  by including the overall minimum of the numeraire portfolio.
Revised: In a continuous-path semimartingale market model with wealth processes discounted by a riskless asset is considered. The numeraire portfolio is the unique strictly positive wealth process that, when used as a benchmark to denominate all other wealth, makes all wealth processes local martingales. It is assumed that the numeraire portfolio exists and that its wealth increases to infinity as time goes to infinity. Under this setting, an initial enlargement of the filtration by including the overall minimum of the numeraire portfolio.
Edit intent: meaning-changed
Original:  A partial converse to the previous result is also established  , showing that the time of the overall minimum of the numeraire portfolio is in a certain sense unique in rendering undesirable the act of undertaking risky positions before it.
Revised:  A partial converse to the previous result is also established in the case of complete markets , showing that the time of the overall minimum of the numeraire portfolio is in a certain sense unique in rendering undesirable the act of undertaking risky positions before it.
Edit intent: meaning-changed
Original:  Assuming Brownian market self-similarity, the market return  memory and autocorrelation functions are derived, which exhibit an oscillatory-decaying behavior and a long-time tail similar to the empirical observations .
Revised:  Assuming market Brownian self-similarity, the market return memory and autocorrelation functions are derived, which exhibit an oscillatory-decaying behavior and a long-time tail similar to the empirical observations .
Edit intent: fluency
Original:  Assuming Brownian market self-similarity, the market return  memory and autocorrelation functions are derived, which exhibit an oscillatory-decaying behavior and a long-time tail similar to the empirical observations .
Revised:  Assuming Brownian market self-similarity, the market return rate memory and autocorrelation functions are derived, which exhibit an oscillatory-decaying behavior and a long-time tail similar to the empirical observations .
Edit intent: meaning-changed
Original:  Assuming Brownian market self-similarity, the market return  memory and autocorrelation functions are derived, which exhibit an oscillatory-decaying behavior and a long-time tail similar to the empirical observations .
Revised:  Assuming Brownian market self-similarity, the market return memory and autocorrelation functions are derived, which exhibit an oscillatory-decaying behavior with a long-time tail similar to the empirical observations .
Edit intent: fluency
Original:  Assuming Brownian market self-similarity, the market return  memory and autocorrelation functions are derived, which exhibit an oscillatory-decaying behavior and a long-time tail similar to the empirical observations .
Revised:  Assuming Brownian market self-similarity, the market return memory and autocorrelation functions are derived, which exhibit an oscillatory-decaying behavior and a long-time tail , similar to empirical observations. Individual stocks are also described via the generalized Langevin equation. They are classified by their relation to the market memory as heavy, neutral and light stocks, possessing different kinds of autocorrelation functions .
Edit intent: meaning-changed
Original: Cells sense external signal constantly, process it, and make its life-determining decision by using the embedded signal processing facilities. All of those events take place within an individual cell and thus should be studied at the level of single cells. Technical advances in live cell imaging make it possible to observe the time evolution of a protein abundance in single cells. Here we use a computational model, live cell fluorescence microscopy, and quantitative RT-PCR to investigate the translocation dynamics of a protein NF-kB and its biological relevance in single macrophages (RAW264.7 cells) when the cells are stimulated by E. coli lipopolysaccharide persistently. We incorporate into the computational model the signaling pathways of TLR4-MyD88-NF-kB, TNF-R and TNFa autocrine signaling and simulate heterogeneous NF-kB response in single cells, by taking into account the cell-to-cell variability in key protein copy numbers and kinetic rate constants. We present the fascinating yet puzzling NF-kB translocation dynamics as a response to different dosage of E. coli lipopolysaccharide: homogeneous oscillatory patterns of NF-kB for a large dosage and heterogeneous monotone-increasing patterns for a small dosage .
Revised: This paper has been withdrawn by the author .
Edit intent: meaning-changed
Original:  By analyzing the Riccati system, which is associated with the affine process via the transform formula, we fully characterize the regions of exponents in which asset price moments do not explode at any time or explode at a given time.
Revised:  By analyzing the Riccati system, which is associated with the affine process via the transform formula, we fully characterize the regions of exponents in which exponential moments of a given process do not explode at any time or explode at a given time.
Edit intent: clarity
Original:  These behaviors are closely tied to the long-term growth rate of asset price momentsas well as implied volatility asymptotics at large-time-to-maturity or at extreme strikes for any given option maturity .
Revised:  In these two cases, we also compute the long-term growth rate of asset price momentsas well as implied volatility asymptotics at large-time-to-maturity or at extreme strikes for any given option maturity .
Edit intent: clarity
Original:  These behaviors are closely tied to the long-term growth rate of asset price momentsas well as implied volatility asymptotics at large-time-to-maturity or at extreme strikes for any given option maturity .
Revised:  These behaviors are closely tied to the long-term growth rate and the explosion rate for exponential moments. These results provide a handle to study implied volatility asymptotics at large-time-to-maturity or at extreme strikes for any given option maturity .
Edit intent: meaning-changed
Original:  These behaviors are closely tied to the long-term growth rate of asset price momentsas well as implied volatility asymptotics at large-time-to-maturity or at extreme strikes for any given option maturity .
Revised:  These behaviors are closely tied to the long-term growth rate of asset price momentsas well as implied volatility asymptotics in models where return of stock prices are modeled by affine processes whose exponential moments do not have an explicit formula .
Edit intent: meaning-changed
Original: I apply the method of planar diagrammatic expansion  to solve the problem of finding the mean spectral density of the  non-Hermitian time-lagged covariance estimator for a system of i.i.d. Gaussian random variables .
Revised: I apply the method of planar diagrammatic expansion - introduced in a self-consistent way - to solve the problem of finding the mean spectral density of the non-Hermitian time-lagged covariance estimator for a system of i.i.d. Gaussian random variables .
Edit intent: meaning-changed
Original: I apply the method of planar diagrammatic expansion  to solve the problem of finding the mean spectral density of the  non-Hermitian time-lagged covariance estimator for a system of i.i.d. Gaussian random variables .
Revised: I apply the method of planar diagrammatic expansion to solve the problem of finding the mean spectral density of the Hermitian equal-time and non-Hermitian time-lagged covariance estimator for a system of i.i.d. Gaussian random variables .
Edit intent: meaning-changed
Original: I apply the method of planar diagrammatic expansion  to solve the problem of finding the mean spectral density of the  non-Hermitian time-lagged covariance estimator for a system of i.i.d. Gaussian random variables .
Revised: I apply the method of planar diagrammatic expansion to solve the problem of finding the mean spectral density of the non-Hermitian time-lagged cross-covariance estimators, for systems of Gaussian random variables .
Edit intent: clarity
Original: I apply the method of planar diagrammatic expansion  to solve the problem of finding the mean spectral density of the  non-Hermitian time-lagged covariance estimator for a system of i.i.d. Gaussian random variables . I confirm the result in a much simpler way using a recent conjecture about non-Hermitian random matrix modelswith rotationally-symmetric spectra. I conjecture and test numerically a form of finite-size corrections to the mean spectral density featuring the complementary error function .
Revised: I apply the method of planar diagrammatic expansion to solve the problem of finding the mean spectral density of the non-Hermitian time-lagged covariance estimator for a system of i.i.d. Gaussian random variables with various underlying covariance functions, both writing the general equations and applying them to several toy models. The models aim at a more and more accurate description of complex financial systems - to which a lengthy introduction is given - albeit only within the Gaussian approximation .
Edit intent: meaning-changed
Original: I apply the method of planar diagrammatic expansion - introduced in a self-consistent way - to solve the problem of finding the mean spectral density of the Hermitian equal-time and non-Hermitian time-lagged cross-covariance estimators, for systems of Gaussian random variables with various underlying covariance functions, both writing the general equations and applying them to several toy models.
Revised: The random matrix theory method of planar diagrammatic expansion - introduced in a self-consistent way - to solve the problem of finding the mean spectral density of the Hermitian equal-time and non-Hermitian time-lagged cross-covariance estimators, for systems of Gaussian random variables with various underlying covariance functions, both writing the general equations and applying them to several toy models.
Edit intent: meaning-changed
Original: I apply the method of planar diagrammatic expansion - introduced in a self-consistent way - to solve the problem of finding the mean spectral density of the Hermitian equal-time and non-Hermitian time-lagged cross-covariance estimators, for systems of Gaussian random variables with various underlying covariance functions, both writing the general equations and applying them to several toy models.
Revised: I apply the method of planar Gaussian diagrammatic expansion is applied to find the mean spectral density of the Hermitian equal-time and non-Hermitian time-lagged cross-covariance estimators, for systems of Gaussian random variables with various underlying covariance functions, both writing the general equations and applying them to several toy models.
Edit intent: clarity
Original: I apply the method of planar diagrammatic expansion - introduced in a self-consistent way - to solve the problem of finding the mean spectral density of the Hermitian equal-time and non-Hermitian time-lagged cross-covariance estimators, for systems of Gaussian random variables with various underlying covariance functions, both writing the general equations and applying them to several toy models. The models aim at a more and more accurate description of complex financial systems - to which a lengthy introduction is given - albeit only within the Gaussian approximation .
Revised: I apply the method of planar diagrammatic expansion - introduced in a self-consistent way - to solve the problem of finding the mean spectral density of the Hermitian equal-time and non-Hermitian time-lagged cross-covariance estimators, firstly in the form of master equations for the most general multivariate Gaussian system, secondly for seven particular toy models of the true covariance function. For the simplest one of these models, the existing result is shown to be incorrect and the right one is presented, moreover its generalizations are accomplished to the exponentially-weighted moving average estimator as well as two non-Gaussian distributions, Student t and free Levy. The paper revolves around applications to financial complex systems, and the results constitute a sensitive probe of the true correlations present there .
Edit intent: meaning-changed
Original: We show that the notion of induction introduced by Cassaigne, Ferenczi and Zamboni for trees of relations arising in the context of interval exchange relations can be generalised to the case of an arbitrary number of possible edge labels. We prove that the equivalence classes of its transitive closure can still be characterised via a circular order on the trees of relations in this case. We compute the cardinalities of these equivalence classes and show that the sequence of cardinalities, for a fixed number of possible edge labels, is a convolution of a Fuss-Catalan sequence. As in the original case, the equivalence classes are in bijection with a set of pseudoknot-free secondary structures arising from the study of RNA; we show that a natural subset of this set is in bijection with a set of m-clusters (in the cluster algebra sense).
Revised: We develop and study the structure of combinatorial objects arising from interval exchange transformations. We classify and enumerate these objects and further show that a natural subset of this set is in bijection with a set of m-clusters (in the cluster algebra sense).
Edit intent: clarity
Original: We develop and study the structure of combinatorial objects  arising from interval exchange transformations . We classify and enumerate these objects and further show that a natural subset of these objects is in natural bijection with a set of m-clusters (in the cluster algebra sense) .
Revised: We develop and study the structure of combinatorial objects arising from interval exchange transformations generalising those in the Sturmian context. We represent them as labelled edge-coloured trees. We classify and enumerate these objects and further show that a natural subset of these objects is in natural bijection with a set of m-clusters (in the cluster algebra sense) .
Edit intent: meaning-changed
Original:  We classify and enumerate these objects and further show that a natural subset of these objects is in natural bijection with a set of m-clusters (in the cluster algebra sense) .
Revised:  We classify and enumerate these objects and further show that a natural subset of these objects is in natural bijection with a set of m-clusters . Furthermore, we interpret a notion of induction used to model generalised interval exchange transformations as a composition of cluster mutations .
Edit intent: meaning-changed
Original: We develop and study the structure of combinatorial objects that are a special case of RNA secondary structures. These are generalizations of objects arising from interval exchange transformations in work of J. Cassaigne, S. Ferenczi and L. Q. Zamboni. We represent them as labelled edge-coloured trees. We classify and enumerate them and show that a natural subset is in bijection with a set of m-clusters.
Revised: We study a circular order on labelled, m-edge-coloured trees with k vertices, and show that the set of such trees with a fixed circular order is in bijection with the set of RNA m-diagrams of degree k, combinatorial objects which can be regarded as RNA secondary structures of a certain kind. We enumerate these sets and show that a natural subset is in bijection with a set of m-clusters.
Edit intent: clarity
Original:  We classify and enumerate them and show that a natural subset is in bijection with a set of m-clusters. Furthermore, we interpret a notion of induction used to model generalised interval exchange transformations as a composition of cluster mutations .
Revised:  We classify and enumerate them and show that the set of trees with a fixed circular order can be characterized as an equivalence class for the transitive closure of an operation which, in the case m=3, arises as an induction in the context of interval exchange transformations as a composition of cluster mutations .
Edit intent: meaning-changed
Original:  Our results indicate that ectoine and hydroxyectoine are able to bind more water molecules than urea on short scales. Furthermore we investigated the number and appearance of hydrogen bonds between the molecules and the solvent. The simulations show that some specific groups in the compatible solutes are able to form a pronounced ordering of the local water structure.
Revised:  Our results indicate that ectoine and hydroxyectoine are able to bind more water molecules than urea by a pronounced ordering of the local water structure.
Edit intent: coherence