wanyu/IteraTeR_full_sent huggingface dataset:
Original: A symmetry-guided time redefinition may enhance and simplify analyses of historical series displaying recurrent patterns . Enforcing a simple-scaling symmetry with Hurst exponent 1/2 and the requirement of increments' stationarity , we identify a time-definition protocol in the financial case. The novel time scale, constructed through a systematic application of the Kolmogorov-Smirnov criterion to extensive data of the S P500 index, lays a bridge between the regime of minutes and that of several days in physical time.
Revised: A symmetry-guided time redefinition may enhance and simplify analyses of historical series displaying recurrent patterns . Enforcing a simple-scaling symmetry with Hurst exponent 1/2 and the requirement of increments' stationarity , we identify a P500 index, lays a bridge between the regime of minutes and that of several days in physical time.
Edit intent: clarity
Original:  The novel time scale, constructed through a systematic application of the Kolmogorov-Smirnov criterion to extensive data of the S P500 index, lays a bridge between the regime of minutes and that of several days in physical time. It allows us to quantify the duration of periods in which the market is inactive , like amid nights, and to optimally exploit the statistical information contained in the series.
Revised:  The novel time scale, constructed through a systematic application of the Kolmogorov-Smirnov criterion to extensive data of the S successful protocol of time definition in Finance. The essential structure of the stochastic process underlying the series can thus be analyzed within a most parsimonious symmetry scheme in which multiscaling is reduced in the quest of a time scale additive and independent of moment-order in the distribution of returns. At the same time, duration of periods in which the market is inactive , like amid nights, and to optimally exploit the statistical information contained in the series.
Edit intent: meaning-changed
Original:  It allows us to quantify the duration of periods in which the market is inactive , like amid nights, and to optimally exploit the statistical information contained in the series.The overall strategy leads to a significant reduction of multiscaling features, once the moments of the return probability density function are analyzed versus the novel time .
Revised:  It allows us to quantify the duration of periods in which markets remain inactive are properly quantified by the novel clock, and the corresponding (e.g., overnight) returns are consistently taken into account for financial applications .
Edit intent: clarity
Original: We introduce a tensor-based algebraic clustering method to extract sparse, low-dimensional structure from multidimensional arrays of experimental data. Our methodology is applicable to high dimensional data structures that arise across the sciences. Specifically we introduce a new way to cluster data subject to multi-indexed structural constraints via integer programming. The method can work as a stand-alone clustering tool or in combination with established methods. We implement this approach on a dataset consisting of genetically diverse breast cancer cell lines exposed to a range of signaling molecules, where each experiment is labelled by its combination of cell line and ligand.
Revised: We introduce a tensor-based algebraic clustering method to extract sparse, low-dimensional structure from high-dimensional, multi-indexed datasets. Specifically, this framework is designed to enable detection of clusters of data in the presence of structural requirements which we encode as algebraic constraints in a linear program. We illustrate our method on a collection of experiments measuring the response of genetically diverse breast cancer cell lines exposed to a range of signaling molecules, where each experiment is labelled by its combination of cell line and ligand.
Edit intent: clarity
Original:  We implement this approach on a dataset consisting of genetically diverse breast cancer cell lines exposed to a range of signaling molecules, where each experiment is labelled by its combination of cell line and ligand. The data consist of time-course measurements of the immediate-early signaling of mitogen activated protein kinase (MAPK ), and phosphoinositide 3-kinase (PI3K)/Protein kinase B (AKT ).
Revised:  We implement this approach on a dataset consisting of genetically diverse breast cancer cell lines to an array of ligands. Each experiment consists of a cell line-ligand combination, and contains time-course measurements of the immediate-early signaling of mitogen activated protein kinase (MAPK ), and phosphoinositide 3-kinase (PI3K)/Protein kinase B (AKT ).
Edit intent: clarity
Original:  The data consist of time-course measurements of the immediate-early signaling of mitogen activated protein kinase (MAPK ), and phosphoinositide 3-kinase (PI3K)/Protein kinase B (AKT ). By respecting the multi-indexed structure of the experimental data, the analysis can be optimized for biological interpretation and therapeutic understanding.
Revised:  The data consist of time-course measurements of the early-signalling kinases MAPK and AKT at two different ligand dose levels. By imposing appropriate structural constraints and respecting the multi-indexed structure of the experimental data, the analysis can be optimized for biological interpretation and therapeutic understanding.
Edit intent: meaning-changed
Original:  We  quantify the heterogeneity of breast cancer cell subtypes and systematically explore mechanistic models of MAP Kinase and PI3K (phosphoinositide 3-kinase)/AKT crosstalk based on the results of our method .
Revised:  We then perform a systematic, large-scale exploration of mechanistic models of MAPK-AKT crosstalk for each cluster. This analysis allows us to quantify the heterogeneity of breast cancer cell subtypes and systematically explore mechanistic models of MAP Kinase and PI3K (phosphoinositide 3-kinase)/AKT crosstalk based on the results of our method .
Edit intent: meaning-changed
Original:  We  quantify the heterogeneity of breast cancer cell subtypes and systematically explore mechanistic models of MAP Kinase and PI3K (phosphoinositide 3-kinase)/AKT crosstalk based on the results of our method .
Revised:  We quantify the heterogeneity of breast cancer cell subtypes , and leads to hypotheses about the mechanisms by which cell lines respond to ligands. Our clustering method is general and can be tailored to a variety of applications in science and industry .
Edit intent: clarity
Original:  This analysis allows us to quantify the heterogeneity of breast cancer cell subtypes, and leads to hypotheses about the mechanisms by which cell lines respond to ligands. Our clustering method is general and can be tailored to a variety of applications in science and industry .
Revised:  This analysis allows us to quantify the heterogeneity of breast cancer cell subtypes, and leads to hypotheses about the signalling mechanisms that mediate the response of the cell lines to ligands .
Edit intent: clarity
Original:  For example: the motifs in Feliu-Wiuf'12 , sequential distributive multisite phosphorylation networks, sequential processive multisite phosphorylation networks, most of the examples in Angeli et al. '07 , phosphorylation cascades, two component systems as in Kothamachu et al. '15 , the bacterial EnvZ/OmpR network in Shinar-Feinberg'10 and  all linear networks.
Revised:  For example: the motifs in Feliu and Wiuf (2012a) , sequential distributive multisite phosphorylation networks, sequential processive multisite phosphorylation networks, most of the examples in Angeli et al. '07 , phosphorylation cascades, two component systems as in Kothamachu et al. '15 , the bacterial EnvZ/OmpR network in Shinar-Feinberg'10 and all linear networks.
Edit intent: meaning-changed
Original:  For example: the motifs in Feliu-Wiuf'12 , sequential distributive multisite phosphorylation networks, sequential processive multisite phosphorylation networks, most of the examples in Angeli et al. '07 , phosphorylation cascades, two component systems as in Kothamachu et al. '15 , the bacterial EnvZ/OmpR network in Shinar-Feinberg'10 and  all linear networks.
Revised:  For example: the motifs in Feliu-Wiuf'12 , sequential distributive and processive multisite phosphorylation networks, most of the examples in Angeli et al. '07 , phosphorylation cascades, two component systems as in Kothamachu et al. '15 , the bacterial EnvZ/OmpR network in Shinar-Feinberg'10 and all linear networks.
Edit intent: clarity
Original:  For example: the motifs in Feliu-Wiuf'12 , sequential distributive multisite phosphorylation networks, sequential processive multisite phosphorylation networks, most of the examples in Angeli et al. '07 , phosphorylation cascades, two component systems as in Kothamachu et al. '15 , the bacterial EnvZ/OmpR network in Shinar-Feinberg'10 and  all linear networks.
Revised:  For example: the motifs in Feliu-Wiuf'12 , sequential distributive multisite phosphorylation networks, sequential processive multisite phosphorylation networks, most of the examples in Angeli et al. (2007) , phosphorylation cascades, two component systems as in Kothamachu et al. '15 , the bacterial EnvZ/OmpR network in Shinar-Feinberg'10 and all linear networks.
Edit intent: clarity
Original:  For example: the motifs in Feliu-Wiuf'12 , sequential distributive multisite phosphorylation networks, sequential processive multisite phosphorylation networks, most of the examples in Angeli et al. '07 , phosphorylation cascades, two component systems as in Kothamachu et al. '15 , the bacterial EnvZ/OmpR network in Shinar-Feinberg'10 and  all linear networks.
Revised:  For example: the motifs in Feliu-Wiuf'12 , sequential distributive multisite phosphorylation networks, sequential processive multisite phosphorylation networks, most of the examples in Angeli et al. '07 , phosphorylation cascades, two component systems as in Kothamachu et al. (2015) , the bacterial EnvZ/OmpR network in Shinar-Feinberg'10 and all linear networks.
Edit intent: clarity
Original:  For example: the motifs in Feliu-Wiuf'12 , sequential distributive multisite phosphorylation networks, sequential processive multisite phosphorylation networks, most of the examples in Angeli et al. '07 , phosphorylation cascades, two component systems as in Kothamachu et al. '15 , the bacterial EnvZ/OmpR network in Shinar-Feinberg'10 and  all linear networks.
Revised:  For example: the motifs in Feliu-Wiuf'12 , sequential distributive multisite phosphorylation networks, sequential processive multisite phosphorylation networks, most of the examples in Angeli et al. '07 , phosphorylation cascades, two component systems as in Kothamachu et al. '15 , the bacterial EnvZ/OmpR network in Shinar and Feinberg (2010) all linear networks.
Edit intent: clarity
Original:  For example: the motifs in Feliu-Wiuf'12 , sequential distributive multisite phosphorylation networks, sequential processive multisite phosphorylation networks, most of the examples in Angeli et al. '07 , phosphorylation cascades, two component systems as in Kothamachu et al. '15 , the bacterial EnvZ/OmpR network in Shinar-Feinberg'10 and  all linear networks.
Revised:  For example: the motifs in Feliu-Wiuf'12 , sequential distributive multisite phosphorylation networks, sequential processive multisite phosphorylation networks, most of the examples in Angeli et al. '07 , phosphorylation cascades, two component systems as in Kothamachu et al. '15 , the bacterial EnvZ/OmpR network in Shinar-Feinberg'10 and , and all linear networks.
Edit intent: fluency
Original:  We simplify the study of steady states of these systems by explicit elimination of intermediate complexes  (inspired by Feliu-Wiuf'12 , 13 and Thomson-Gunawardena'09)and we  define an important subclass of MESSI systems with toric steady states .
Revised:  We simplify the study of steady states of these systems by explicit elimination of intermediate complexes and we give conditions to ensure an explicit rational parametrization of the variety of steady states (inspired by Feliu-Wiuf'12 , 13 and Thomson-Gunawardena'09)and we define an important subclass of MESSI systems with toric steady states .
Edit intent: meaning-changed
Original:  We simplify the study of steady states of these systems by explicit elimination of intermediate complexes  (inspired by Feliu-Wiuf'12 , 13 and Thomson-Gunawardena'09)and we  define an important subclass of MESSI systems with toric steady states .
Revised:  We simplify the study of steady states of these systems by explicit elimination of intermediate complexes (inspired by Feliu and Wiuf (2013a , 13 and Thomson-Gunawardena'09)and we define an important subclass of MESSI systems with toric steady states .
Edit intent: meaning-changed
Original:  We simplify the study of steady states of these systems by explicit elimination of intermediate complexes  (inspired by Feliu-Wiuf'12 , 13 and Thomson-Gunawardena'09)and we  define an important subclass of MESSI systems with toric steady states .
Revised:  We simplify the study of steady states of these systems by explicit elimination of intermediate complexes (inspired by Feliu-Wiuf'12 , 2013b), Thomson and Gunawardena (2009) define an important subclass of MESSI systems with toric steady states .
Edit intent: meaning-changed
Original:  We simplify the study of steady states of these systems by explicit elimination of intermediate complexes  (inspired by Feliu-Wiuf'12 , 13 and Thomson-Gunawardena'09)and we  define an important subclass of MESSI systems with toric steady states .
Revised:  We simplify the study of steady states of these systems by explicit elimination of intermediate complexes (inspired by Feliu-Wiuf'12 , 13 and Thomson-Gunawardena'09)and we ). We define an important subclass of MESSI systems with toric steady states .
Edit intent: fluency
Original:  We simplify the study of steady states of these systems by explicit elimination of intermediate complexes  (inspired by Feliu-Wiuf'12 , 13 and Thomson-Gunawardena'09)and we  define an important subclass of MESSI systems with toric steady states . We  give for MESSI systems with toric steady states an easy algorithm to determine the capacity for multistationarity.
Revised:  We simplify the study of steady states of these systems by explicit elimination of intermediate complexes (inspired by Feliu-Wiuf'12 , 13 and Thomson-Gunawardena'09)and we define an important subclass of MESSI systems with toric steady states P\'erez Mill\'an et al. (2012) give for MESSI systems with toric steady states an easy algorithm to determine the capacity for multistationarity.
Edit intent: meaning-changed
Original: We fully characterize discrete-time dynamic convex expectations (\mathcal{E }  upper semianalytic functions - in particular we work without a reference measure and do not assume essential suprema to exist.
Revised: Given two Polish spaces U and V, denote by \mathcal{L } upper semianalytic functions - in particular we work without a reference measure and do not assume essential suprema to exist.
Edit intent: meaning-changed
Original: We fully characterize discrete-time dynamic convex expectations (\mathcal{E }  upper semianalytic functions - in particular we work without a reference measure and do not assume essential suprema to exist.
Revised: We fully characterize discrete-time dynamic convex expectations (\mathcal{E \times} upper semianalytic functions - in particular we work without a reference measure and do not assume essential suprema to exist.
Edit intent: meaning-changed
Original: We fully characterize discrete-time dynamic convex expectations (\mathcal{E }  upper semianalytic functions - in particular we work without a reference measure and do not assume essential suprema to exist.
Revised: We fully characterize discrete-time dynamic convex expectations (\mathcal{E } V) and \mathcal{L upper semianalytic functions - in particular we work without a reference measure and do not assume essential suprema to exist.
Edit intent: meaning-changed
Original: We fully characterize discrete-time dynamic convex expectations (\mathcal{E }  upper semianalytic functions - in particular we work without a reference measure and do not assume essential suprema to exist. It is shown that \mathcal{E } (\cdot|U)}\colon }\to(U) be a sublinear increasing functional which leaves L(U) invariant.
Revised: We fully characterize discrete-time dynamic convex expectations (\mathcal{E } upper semianalytic functions from U } (\cdot|U)}\colon }\to(U) be a sublinear increasing functional which leaves L(U) invariant.
Edit intent: coherence
Original:  It is shown that \mathcal{E } (\cdot|U)}\colon }\to(U) be a sublinear increasing functional which leaves L(U) invariant.
Revised:  It is shown that \mathcal{E \times} (\cdot|U)}\colon }\to(U) be a sublinear increasing functional which leaves L(U) invariant.
Edit intent: meaning-changed
Original:  It is shown that \mathcal{E } (\cdot|U)}\colon }\to(U) be a sublinear increasing functional which leaves L(U) invariant.
Revised:  It is shown that \mathcal{E } V and U to the real line, respectively. Let \mathcal{E(\cdot|U)}\colon }\to(U) be a sublinear increasing functional which leaves L(U) invariant.
Edit intent: meaning-changed
Original:  It is shown that \mathcal{E } (\cdot|U)}\colon }\to(U) be a sublinear increasing functional which leaves L(U) invariant.
Revised:  It is shown that \mathcal{E } (\cdot|U)}\colon\mathcal{L }\to(U) be a sublinear increasing functional which leaves L(U) invariant.
Edit intent: meaning-changed
Original:  It is shown that \mathcal{E } (\cdot|U)}\colon }\to(U) be a sublinear increasing functional which leaves L(U) invariant.
Revised:  It is shown that \mathcal{E } (\cdot|U)}\colon \times}\to(U) be a sublinear increasing functional which leaves L(U) invariant.
Edit intent: meaning-changed
Original:  It is shown that \mathcal{E } (\cdot|U)}\colon }\to(U) be a sublinear increasing functional which leaves L(U) invariant.
Revised:  It is shown that \mathcal{E } (\cdot|U)}\colon }V)\to(U) be a sublinear increasing functional which leaves L(U) invariant.
Edit intent: meaning-changed
Original:  It is shown that \mathcal{E } (\cdot|U)}\colon }\to(U) be a sublinear increasing functional which leaves L(U) invariant.
Revised:  It is shown that \mathcal{E } (\cdot|U)}\colon }\to\mathcal{L(U) be a sublinear increasing functional which leaves L(U) invariant.
Edit intent: meaning-changed
Original:  if and only if \mathcal{E}(\cdot |U) } is pointwise continuous from below and continuous from above on the continuous functions if and only if a dual representation of \mathcal{E_t in terms of conditional expectations minus the convex conjugate of \mathcal{E}_t holds true, where the conjugate is lower semianalytic with pointwise weakly compact level sets.
Revised:  if and only if \mathcal{E}(\cdot |U) } is pointwise continuous from below and continuous from above on the continuous functions _t in terms of conditional expectations minus the convex conjugate of \mathcal{E}_t holds true, where the conjugate is lower semianalytic with pointwise weakly compact level sets.
Edit intent: clarity
Original:  Moreover, we provide a dual characterization of the dynamic property , i.e. we show that \mathcal{E}_t} (\cdot)}\colon } \to which leaves the constants invariant, the tower property \mathcal{E}(\cdot)} =\mathcal{E} _t\circ\mathcal{E_{t+1} if and only if the convex conjugate of \mathcal{E}_t has an additive form.
Revised:  Moreover, we provide a dual characterization of the dynamic property , i.e. we show that \mathcal{E}_t} . Further, given another sublinear increasing functional \mathcal{E(\cdot)}\colon } \to which leaves the constants invariant, the tower property \mathcal{E}(\cdot)} =\mathcal{E} _t\circ\mathcal{E_{t+1} if and only if the convex conjugate of \mathcal{E}_t has an additive form.
Edit intent: meaning-changed
Original:  Moreover, we provide a dual characterization of the dynamic property , i.e. we show that \mathcal{E}_t} (\cdot)}\colon } \to which leaves the constants invariant, the tower property \mathcal{E}(\cdot)} =\mathcal{E} _t\circ\mathcal{E_{t+1} if and only if the convex conjugate of \mathcal{E}_t has an additive form.
Revised:  Moreover, we provide a dual characterization of the dynamic property , i.e. we show that \mathcal{E}_t} (\cdot)}\colon\mathcal{L } \to which leaves the constants invariant, the tower property \mathcal{E}(\cdot)} =\mathcal{E} _t\circ\mathcal{E_{t+1} if and only if the convex conjugate of \mathcal{E}_t has an additive form.
Edit intent: meaning-changed
Original:  Moreover, we provide a dual characterization of the dynamic property , i.e. we show that \mathcal{E}_t} (\cdot)}\colon } \to which leaves the constants invariant, the tower property \mathcal{E}(\cdot)} =\mathcal{E} _t\circ\mathcal{E_{t+1} if and only if the convex conjugate of \mathcal{E}_t has an additive form.
Revised:  Moreover, we provide a dual characterization of the dynamic property , i.e. we show that \mathcal{E}_t} (\cdot)}\colon \times} \to which leaves the constants invariant, the tower property \mathcal{E}(\cdot)} =\mathcal{E} _t\circ\mathcal{E_{t+1} if and only if the convex conjugate of \mathcal{E}_t has an additive form.
Edit intent: meaning-changed
Original:  Moreover, we provide a dual characterization of the dynamic property , i.e. we show that \mathcal{E}_t} (\cdot)}\colon } \to which leaves the constants invariant, the tower property \mathcal{E}(\cdot)} =\mathcal{E} _t\circ\mathcal{E_{t+1} if and only if the convex conjugate of \mathcal{E}_t has an additive form.
Revised:  Moreover, we provide a dual characterization of the dynamic property , i.e. we show that \mathcal{E}_t} (\cdot)}\colon } V)\to which leaves the constants invariant, the tower property \mathcal{E}(\cdot)} =\mathcal{E} _t\circ\mathcal{E_{t+1} if and only if the convex conjugate of \mathcal{E}_t has an additive form.
Edit intent: coherence
Original:  Moreover, we provide a dual characterization of the dynamic property , i.e. we show that \mathcal{E}_t} (\cdot)}\colon } \to which leaves the constants invariant, the tower property \mathcal{E}(\cdot)} =\mathcal{E} _t\circ\mathcal{E_{t+1} if and only if the convex conjugate of \mathcal{E}_t has an additive form.
Revised:  Moreover, we provide a dual characterization of the dynamic property , i.e. we show that \mathcal{E}_t} (\cdot)}\colon } \to\mathbb{R which leaves the constants invariant, the tower property \mathcal{E}(\cdot)} =\mathcal{E} _t\circ\mathcal{E_{t+1} if and only if the convex conjugate of \mathcal{E}_t has an additive form.
Edit intent: meaning-changed
Original:  Moreover, we provide a dual characterization of the dynamic property , i.e. we show that \mathcal{E}_t} (\cdot)}\colon } \to which leaves the constants invariant, the tower property \mathcal{E}(\cdot)} =\mathcal{E} _t\circ\mathcal{E_{t+1} if and only if the convex conjugate of \mathcal{E}_t has an additive form.
Revised:  Moreover, we provide a dual characterization of the dynamic property , i.e. we show that \mathcal{E}_t} (\cdot)}\colon } \to which leaves the constants invariant, the tower property \mathcal{E}(\cdot)} =\mathcal{E} _{t+1} if and only if the convex conjugate of \mathcal{E}_t has an additive form.
Edit intent: coherence
Original:  We also consider dynamic convex expectations defined on the set of discrete-time stochastic processes} (\cdot|U)) is characterized via a pasting property of the representing sets of probabilities.
Revised:  We also consider dynamic convex expectations defined on the set of discrete-time stochastic processes} (\mathcal{E(\cdot|U)) is characterized via a pasting property of the representing sets of probabilities.
Edit intent: meaning-changed
Original:  In this paper, we analyze over 4.5 million references to U.S. Federal Acts and Agencies contained within these reports to build a mean-field measurement of temperature and diversity in this regulatory ecosystem  .
Revised:  In this paper, we analyze over 4.5 million references to U.S. Federal Acts and Agencies contained within these reports to build a mean-field measurement of temperature and diversity in this regulatory ecosystem , where companies URLanisms inhabiting the regulatory environment .
Edit intent: meaning-changed