wanyu/IteraTeR_full_sent huggingface dataset:
Original:  As an application, we propose a new estimator that minimizes the(\beta) that may depend on a possibly infinite-dimensional parameter \beta\in }\Bbf\E  ||X(\beta)|| \leq CK }\left( + \gamma_2(}\Bbf\right)(\cdot), and \gamma_2(}\Bbf\Bbf operator norm of the matrix that consists ofthe moment functions. We show the consistency of the estimator .
Revised:  As an application, we propose a new estimator that minimizes the(\beta) that may depend on a possibly infinite-dimensional parameter \beta\in }\Bbf\E ||X(\beta)|| \leq CK }\left( + \gamma_2(}\Bbf\right)(\cdot), and \gamma_2(}\Bbf\Bbf operator norm of moment conditions as well as for estimation of the maximal number of factors with functional data .
Edit intent: meaning-changed
Original:  that may depend on a possibly infinite-dimensional parameter \beta\in %DIFDELCMD < \Bbf%%%  , we obtain a uniform bound on its operator norm of the form %DIFDELCMD < \E %%% \sup \sup} _{\beta \in %DIFDELCMD < \Bbf%%%  } ||X(\beta)|| \leq CK \left(\max(N,T)
Revised:  that may depend on a possibly infinite-dimensional parameter \beta\in %DIFDELCMD < \Bbf%%% \mathbf{B , we obtain a uniform bound on its operator norm of the form %DIFDELCMD < \E %%% \sup \sup} _{\beta \in %DIFDELCMD < \Bbf%%% } ||X(\beta)|| \leq CK \left(\max(N,T)
Edit intent: meaning-changed
Original:  that may depend on a possibly infinite-dimensional parameter \beta\in %DIFDELCMD < \Bbf%%%  , we obtain a uniform bound on its operator norm of the form %DIFDELCMD < \E %%% \sup \sup} _{\beta \in %DIFDELCMD < \Bbf%%%  } ||X(\beta)|| \leq CK \left(\max(N,T)
Revised:  that may depend on a possibly infinite-dimensional parameter \beta\in %DIFDELCMD < \Bbf%%% , we obtain a uniform bound on its operator norm of the form %DIFDELCMD < \E %%% \mathbb{E \sup} _{\beta \in %DIFDELCMD < \Bbf%%% } ||X(\beta)|| \leq CK \left(\max(N,T)
Edit intent: meaning-changed
Original:  that may depend on a possibly infinite-dimensional parameter \beta\in %DIFDELCMD < \Bbf%%%  , we obtain a uniform bound on its operator norm of the form %DIFDELCMD < \E %%% \sup \sup} _{\beta \in %DIFDELCMD < \Bbf%%%  } ||X(\beta)|| \leq CK \left(\max(N,T)
Revised:  that may depend on a possibly infinite-dimensional parameter \beta\in %DIFDELCMD < \Bbf%%% , we obtain a uniform bound on its operator norm of the form %DIFDELCMD < \E %%% \sup \sup} _{\beta \in %DIFDELCMD < \Bbf%%% \mathbf{B } ||X(\beta)|| \leq CK \left(\max(N,T)
Edit intent: meaning-changed
Original:  + \gamma_2( %DIFDELCMD < \Bbf%%% ,d_\Bbf )\right), where C is an absolute constant, K controls the tail behavior of (the increments of) x_{it}(\cdot), and \gamma_2( %DIFDELCMD < \Bbf%%% ,d_\Bbf ) is Talagrand's functional, a measure of multi-scale complexity of the metric space ( %DIFDELCMD < \Bbf%%% ,d_\Bbf ).
Revised:  + \gamma_2( %DIFDELCMD < \Bbf%%% \mathbf{B )\right), where C is an absolute constant, K controls the tail behavior of (the increments of) x_{it}(\cdot), and \gamma_2( %DIFDELCMD < \Bbf%%% ,d_\Bbf ) is Talagrand's functional, a measure of multi-scale complexity of the metric space ( %DIFDELCMD < \Bbf%%% ,d_\Bbf ).
Edit intent: meaning-changed
Original:  + \gamma_2( %DIFDELCMD < \Bbf%%% ,d_\Bbf )\right), where C is an absolute constant, K controls the tail behavior of (the increments of) x_{it}(\cdot), and \gamma_2( %DIFDELCMD < \Bbf%%% ,d_\Bbf ) is Talagrand's functional, a measure of multi-scale complexity of the metric space ( %DIFDELCMD < \Bbf%%% ,d_\Bbf ).
Revised:  + \gamma_2( %DIFDELCMD < \Bbf%%% ,d_\Bbf )\right), where C is an absolute constant, K controls the tail behavior of (the increments of) x_{it}(\cdot), and \gamma_2( %DIFDELCMD < \Bbf%%% \mathbf{B ) is Talagrand's functional, a measure of multi-scale complexity of the metric space ( %DIFDELCMD < \Bbf%%% ,d_\Bbf ).
Edit intent: meaning-changed
Original:  + \gamma_2( %DIFDELCMD < \Bbf%%% ,d_\Bbf )\right), where C is an absolute constant, K controls the tail behavior of (the increments of) x_{it}(\cdot), and \gamma_2( %DIFDELCMD < \Bbf%%% ,d_\Bbf ) is Talagrand's functional, a measure of multi-scale complexity of the metric space ( %DIFDELCMD < \Bbf%%% ,d_\Bbf ).
Revised:  + \gamma_2( %DIFDELCMD < \Bbf%%% ,d_\Bbf )\right), where C is an absolute constant, K controls the tail behavior of (the increments of) x_{it}(\cdot), and \gamma_2( %DIFDELCMD < \Bbf%%% ,d_\Bbf ) is Talagrand's functional, a measure of multi-scale complexity of the metric space ( %DIFDELCMD < \Bbf%%% \mathbf{B ).
Edit intent: meaning-changed
Original:  We develop and analyze features of individual neurons to investigate changes in architectonic differentiation and present a novel high-performance, automated tree-ensemble method trained on data manually labeled by three human investigators. From the location and basic measures of neurons, more complex features are developed and used in machine learning models for automatic segmentation of cortical layers.
Revised:  We develop and analyze features of individual neurons to investigate changes in architectonic differentiation and present a novel high-performance, automated framework for neuron-level histological image analysis. Local tissue and cell descriptors such as density, neuron size and other measures are used for development of more complex neuron features used in machine learning models for automatic segmentation of cortical layers.
Edit intent: meaning-changed
Original:  The most accurate classification results were obtained by training three models separately and creating another ensemble by combining probability outputs for final neuron layer classification. Measurement of importances of developed neuron features on both global model level and individual prediction level are obtained .
Revised:  The most accurate classification results were obtained by training a separate model for each expert and combining their probability outputs. Importances of developed neuron features on both global model level and individual prediction level are obtained .
Edit intent: clarity
Original:  For spiking networks with hierarchical modular topology , we show that slow spike-train fluctuations emerge due to the increase of either  the global synaptic strength parameter or the network hierarchical level , while the network size remains constant.
Revised:  Here we use an information-theoretical approach to investigate activity propagation in spiking networks with hierarchical modular topology , we show that slow spike-train fluctuations emerge due to the increase of either the global synaptic strength parameter or the network hierarchical level , while the network size remains constant.
Edit intent: meaning-changed
Original:  For spiking networks with hierarchical modular topology , we show that slow spike-train fluctuations emerge due to the increase of either  the global synaptic strength parameter or the network hierarchical level , while the network size remains constant.
Revised:  For spiking networks with hierarchical modular topology . We observe that optimized pairwise information propagation emerges due to the increase of either the global synaptic strength parameter or the network hierarchical level , while the network size remains constant.
Edit intent: meaning-changed
Original:  For spiking networks with hierarchical modular topology , we show that slow spike-train fluctuations emerge due to the increase of either  the global synaptic strength parameter or the network hierarchical level , while the network size remains constant.
Revised:  For spiking networks with hierarchical modular topology , we show that slow spike-train fluctuations emerge due to the increase of either (i) the global synaptic strength parameter or the network hierarchical level , while the network size remains constant.
Edit intent: meaning-changed
Original:  For spiking networks with hierarchical modular topology , we show that slow spike-train fluctuations emerge due to the increase of either  the global synaptic strength parameter or the network hierarchical level , while the network size remains constant.
Revised:  For spiking networks with hierarchical modular topology , we show that slow spike-train fluctuations emerge due to the increase of either the global synaptic strength parameter or (ii) the number of modules in the network , while the network size remains constant.
Edit intent: clarity
Original:  Through an information-theoretical approach we show that information propagation of activity among adjacent modules is enhanced as the number of modules increases until an optimal value is reached and then decreases . This suggests that there is an optimal interplay between hierarchical level and synaptic strengths for information propagation among modules, but we also found that information transfer measured from the spike-trains differs from this one indicating that URLanization restructures information communicated in the mesoscopic level .
Revised:  Through an information-theoretical approach we show that information propagation of activity among adjacent modules is enhanced as the number of modules increases until an optimal value is reached and then decreases , showing that there is an optimal interplay between hierarchical level and synaptic strengths for information propagation among modules, but we also found that information transfer measured from the spike-trains differs from this one indicating that URLanization restructures information communicated in the mesoscopic level .
Edit intent: coherence
Original:  This suggests that there is an optimal interplay between hierarchical level and synaptic strengths for information propagation among modules, but we also found that information transfer measured from the spike-trains differs from this one indicating that URLanization restructures information communicated in the mesoscopic level .
Revised:  This suggests that there is an optimal interplay between synaptic strength and modularity for population information flow. This is in contrast to information propagation evaluated among pairs of neurons, which attains maximum value at the maximum values of these two parameter ranges .
Edit intent: clarity
Original:  By examining the  increase of synaptic strengths and number of modules we find that the network behavior changes following different mechanisms: (1 ) increase of autocorrelations among individual neurons, and ( 2 ) increase of cross-correlations among pairs of neurons , respectively.
Revised:  By examining the network behavior under increase of synaptic strengths and number of modules we find that the network behavior changes following different mechanisms: (1 ) increase of autocorrelations among individual neurons, and ( 2 ) increase of cross-correlations among pairs of neurons , respectively.
Edit intent: clarity
Original:  By examining the  increase of synaptic strengths and number of modules we find that the network behavior changes following different mechanisms: (1 ) increase of autocorrelations among individual neurons, and ( 2 ) increase of cross-correlations among pairs of neurons , respectively.
Revised:  By examining the increase of synaptic strength and number of modules we find that the network behavior changes following different mechanisms: (1 ) increase of autocorrelations among individual neurons, and ( 2 ) increase of cross-correlations among pairs of neurons , respectively.
Edit intent: fluency
Original:  By examining the  increase of synaptic strengths and number of modules we find that the network behavior changes following different mechanisms: (1 ) increase of autocorrelations among individual neurons, and ( 2 ) increase of cross-correlations among pairs of neurons , respectively.
Revised:  By examining the increase of synaptic strengths and number of modules we find that these increases are associated with two different effects: (i ) increase of autocorrelations among individual neurons, and ( 2 ) increase of cross-correlations among pairs of neurons , respectively.
Edit intent: clarity
Original:  By examining the  increase of synaptic strengths and number of modules we find that the network behavior changes following different mechanisms: (1 ) increase of autocorrelations among individual neurons, and ( 2 ) increase of cross-correlations among pairs of neurons , respectively.
Revised:  By examining the increase of synaptic strengths and number of modules we find that the network behavior changes following different mechanisms: (1 ) increase of autocorrelations among individual neurons, and ( ii ) increase of cross-correlations among pairs of neurons , respectively.
Edit intent: clarity
Original:  By examining the  increase of synaptic strengths and number of modules we find that the network behavior changes following different mechanisms: (1 ) increase of autocorrelations among individual neurons, and ( 2 ) increase of cross-correlations among pairs of neurons , respectively. The latter being better for information propagation .
Revised:  By examining the increase of synaptic strengths and number of modules we find that the network behavior changes following different mechanisms: (1 ) increase of autocorrelations among individual neurons, and ( 2 ) increase of cross-correlations among pairs of neurons .
Edit intent: clarity
Original:  Based on comprehensive review and comparison study on representative OT and CRDT solutions and working co-editors based on them , we present our main research discoveries in relation to this question and beyond in a series of three related and complementary articles.
Revised:  To seek truth from facts, we set out to conduct a comprehensive and critical review of representative OT and CRDT solutions and working co-editors based on them , we present our main research discoveries in relation to this question and beyond in a series of three related and complementary articles.
Edit intent: meaning-changed
Original:  Based on comprehensive review and comparison study on representative OT and CRDT solutions and working co-editors based on them , we present our main research discoveries in relation to this question and beyond in a series of three related and complementary articles.
Revised:  Based on comprehensive review and comparison study on representative OT and CRDT solutions and working co-editors based on them . From this work, we have made important discoveries about OT and CRDT, and revealed facts and evidences that refute CRDT claims over OT on all accounts. We present our discoveries in three related and complementary articles.
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Original:  In this article, we examine the role of building working co-editors in  OT and CRDT research , and the consequential differences in the adoption of and choice between OT and CRDT in real world co-editors and industry products.
Revised:  In this article, we examine the role of building working co-editors in shaping OT and CRDT research , and the consequential differences in the adoption of and choice between OT and CRDT in real world co-editors and industry products.
Edit intent: clarity
Original:  In this article, we examine the role of building working co-editors in  OT and CRDT research , and the consequential differences in the adoption of and choice between OT and CRDT in real world co-editors and industry products.
Revised:  In this article, we examine the role of building working co-editors in OT and CRDT research and solutions, and consequential differences in the adoption of and choice between OT and CRDT in real world co-editors and industry products.
Edit intent: meaning-changed
Original:  In this article, we examine the role of building working co-editors in  OT and CRDT research , and the consequential differences in the adoption of and choice between OT and CRDT in real world co-editors and industry products.
Revised:  In this article, we examine the role of building working co-editors in OT and CRDT research , and the consequential differences in the choice between OT and CRDT in real world co-editors and industry products.
Edit intent: clarity
Original:  Follow-up CRDT variations are commonly labeled as "post-OT" techniques and have made broad claims of superiority over OT , in terms of correctness, time and space complexity, etc .
Revised:  Follow-up CRDT variations are commonly labeled as "post-OT" techniques capable of making concurrent operations natively commutative in co-editors. On top of that, CRDT solutions have made broad claims of superiority over OT , in terms of correctness, time and space complexity, etc .
Edit intent: meaning-changed
Original:  Follow-up CRDT variations are commonly labeled as "post-OT" techniques and have made broad claims of superiority over OT , in terms of correctness, time and space complexity, etc .
Revised:  Follow-up CRDT variations are commonly labeled as "post-OT" techniques and have made broad claims of superiority over OT solutions, and routinely portrayed OT as an incorrect, complex and inefficient technique .
Edit intent: meaning-changed
Original:  A thorough examination of these questions is relevant not only to researchers exploring the frontiers of co-editing technologies, but also to practitioners seeking viable techniques to build real world applications. Based on comprehensive reviews on representative OT and CRDT solutions and working co-editors based on them , we present our discoveries , in relation to these questions and beyond, in three articles.
Revised:  To seek truth from facts, we set out to conduct a comprehensive and critical review on representative OT and CRDT solutions and working co-editors based on them , we present our discoveries , in relation to these questions and beyond, in three articles.
Edit intent: clarity
Original:  Based on comprehensive reviews on representative OT and CRDT solutions and working co-editors based on them , we present our discoveries , in relation to these questions and beyond, in three articles. We also reveal facts and present evidences that refute CRDT claimed advantages over OT .
Revised:  Based on comprehensive reviews on representative OT and CRDT solutions and working co-editors based on them . From this work, we have made important discoveries about OT and CRDT, and revealed facts and evidences that refute CRDT claimed advantages over OT .
Edit intent: clarity
Original: We make use of a family of primitive securities, in the spirit of Arrow-Debreu, to price and hedge in a model-free way path-dependent exotic derivatives in discrete time. These primitive securities are called signature payoffs. First, we show that cash flows of exotic derivatives in discrete time can be approximated arbitrarily well by these primitive securities, and we then conclude that signature payoffs can be used to price path-dependent exotic derivatives.
Revised: We make use of a family of primitive securities, in the spirit of Arrow-Debreu, to price and hedge in a model-free setting when the trader has access to market prices of a rich enough class of exotic and vanilla options. This is achieved by estimating an unobservable quantity called "implied expected signature" from such market prices, which are used to price path-dependent exotic derivatives.
Edit intent: meaning-changed
Original:  First, we show that cash flows of exotic derivatives in discrete time can be approximated arbitrarily well by these primitive securities, and we then conclude that signature payoffs can be used to price path-dependent exotic derivatives.
Revised:  First, we show that cash flows of exotic derivatives in discrete time can be approximated arbitrarily well by these primitive securities, and we then conclude that signature payoffs can be used to price other exotic derivatives.
Edit intent: meaning-changed
Original:  Second, signature payoffs are used to derive a numerically feasible methodology to dynamically hedging exotic derivatives. It turns out that the only information one needs about the market to dynamically hedge exotic derivatives is the prices of these signature payoffs. These two aspects lead to a model-free approach to numerically price and hedge exotic derivatives from market data - more specifically, from market prices of other exotic derivatives. We demonstrate the feasibility of our approach in several numerical experiments .
Revised:  The implied expected signature is an object that characterises the market dynamics .
Edit intent: clarity
Original:  Here we analyze the dynamics of heterogeneous populations of quadratic integrate-and-fire (QIF) neurons with both chemical and electrical coupling. To this aim, we derive an exact firing rate model that describes the collective dynamics of the QIF network in a unified framework valid for both electrical and chemical coupling.
Revised:  Here we analyze the dynamics of heterogeneous populations of quadratic integrate-and-fire (QIF) neurons with both chemical and electrical synapses. The mathematical analysis of the firing rate model that describes the collective dynamics of the QIF network in a unified framework valid for both electrical and chemical coupling.
Edit intent: clarity
Original:  To this aim, we derive an exact firing rate model that describes the collective dynamics of the QIF network in a unified framework valid for both electrical and chemical coupling. Networks with instantaneous chemical synapsesdisplay a well-known bifurcation scenario characterized by a codimension-2 Cusp point and , thus, by the presence of persistent asynchronous states for strong  excitatory coupling.
Revised:  To this aim, we derive an exact firing rate model reveals a well-established bifurcation scenario for networks with chemical synapses, characterized by a codimension-2 Cusp point and , thus, by the presence of persistent asynchronous states for strong excitatory coupling.
Edit intent: clarity
Original:  Networks with instantaneous chemical synapsesdisplay a well-known bifurcation scenario characterized by a codimension-2 Cusp point and , thus, by the presence of persistent asynchronous states for strong  excitatory coupling.
Revised:  Networks with instantaneous chemical synapsesdisplay a well-known bifurcation scenario characterized by a codimension-2 Cusp point and persistent states for strong excitatory coupling.
Edit intent: coherence
Original:  Networks with instantaneous chemical synapsesdisplay a well-known bifurcation scenario characterized by a codimension-2 Cusp point and , thus, by the presence of persistent asynchronous states for strong  excitatory coupling.
Revised:  Networks with instantaneous chemical synapsesdisplay a well-known bifurcation scenario characterized by a codimension-2 Cusp point and , thus, by the presence of persistent asynchronous states for strong recurrent excitatory coupling.
Edit intent: meaning-changed
Original:  The inclusion of electrical coupling generally implies the emergence of a supercritical Hopf bifurcation and, hence, neuronal synchrony. This dramatically transforms the Cusp scenario into a bifurcation scenario characterized by three codimension-2 points (Cusp, Takens-Bogdanov, and Saddle-Node Separatrix Loop), which  is generic for the dynamics of heterogeneous QIF networks with both chemical and electrical  coupling.
Revised:  The inclusion of electrical coupling generally implies the emergence of a supercritical Hopf bifurcation . This transforms the Cusp scenario into a bifurcation scenario characterized by three codimension-2 points (Cusp, Takens-Bogdanov, and Saddle-Node Separatrix Loop), which is generic for the dynamics of heterogeneous QIF networks with both chemical and electrical coupling.
Edit intent: clarity
Original:  This dramatically transforms the Cusp scenario into a bifurcation scenario characterized by three codimension-2 points (Cusp, Takens-Bogdanov, and Saddle-Node Separatrix Loop), which  is generic for the dynamics of heterogeneous QIF networks with both chemical and electrical  coupling.
Revised:  This dramatically transforms the Cusp scenario into a bifurcation scenario characterized by three codimension-2 points (Cusp, Takens-Bogdanov, and Saddle-Node Separatrix Loop), which greatly reduces the possibility for persistent states. This is generic for the dynamics of heterogeneous QIF networks with both chemical and electrical coupling.
Edit intent: meaning-changed