wanyu/IteraTeR_full_sent huggingface dataset:
Original:  This includes phase-locking , as seen in Chlamydomonas flagella {\it  , and metachronal wave formation in the ciliary arrays of Paramecium or in the respiratory cilia of URLanisms.
Revised:  This includes phase-locking , as seen in Chlamydomonas flagella {\it Chlamydomonas , and metachronal wave formation in the ciliary arrays of Paramecium or in the respiratory cilia of URLanisms.
Edit intent: meaning-changed
Original:  This includes phase-locking , as seen in Chlamydomonas flagella {\it  , and metachronal wave formation in the ciliary arrays of Paramecium or in the respiratory cilia of URLanisms.
Revised:  This includes phase-locking , as seen in Chlamydomonas flagella {\it , and metachronal wave formation in the respiratory cilia of URLanisms.
Edit intent: clarity
Original:  Recent work on the dynamics of physically separated pairs of flagella isolated from the multicellular alga Volvox {\it  has shown that hydrodynamic coupling alone is sufficient to produce synchrony.
Revised:  Recent work on the dynamics of physically separated pairs of flagella isolated from the multicellular alga Volvox {\it Volvox has shown that hydrodynamic coupling alone is sufficient to produce synchrony.
Edit intent: meaning-changed
Original:  The situation is more complex when considering multiple flagellaon a single cell. Specifically, the unicellular biflagellate Chlamydomonasswims with opposing power strokes, yet synchronizes in phase in the familiar breaststroke. This indicates{\it   that a mechanism, internal to the cell, provides an additional flagellar coupling.
Revised:  The situation is more complex in URLanisms bearing few flagella. We show that flagella of{\it that a mechanism, internal to the cell, provides an additional flagellar coupling.
Edit intent: clarity
Original:  Here we show that in comparison to the wildtype, markedly different synchronization states are found in Chlamydomonas mutants deficient in filamentary connections between basal bodies. Quantitative studies of complex flagellar coordination strategies found in quadri-, octo- and hexadecaflagellates reveal further evidence that intracellular couplings between flagellar basal bodies compete with hydrodynamic interactions to determine the precise form of flagellar synchronization in unicellular algae.
Revised:  In naturally occurring species with 4, 8, or even 16 flagella, we find diverse symmetries of basal body positioning and of the flagellar apparatus that are coincident with specific gaits of flagellar actuation, suggesting that it is a competition between intracellular coupling and hydrodynamic interactions that ultimately determines the precise form of flagellar synchronization in unicellular algae.
Edit intent: clarity
Original:  Quantitative studies of complex flagellar coordination strategies found in quadri-, octo- and hexadecaflagellates reveal further evidence that intracellular couplings between flagellar basal bodies compete with hydrodynamic interactions to determine the precise form of flagellar synchronization in unicellular algae.
Revised:  Quantitative studies of complex flagellar coordination strategies found in quadri-, octo- and hexadecaflagellates reveal further evidence that intracellular couplings between flagellar basal bodies compete with hydrodynamic interactions to determine the precise form of flagellar coordination in unicellular algae.
Edit intent: fluency
Original: In this paper we consider a market model where there are two levels of information , the public information generated by the financial assets  and a larger flow of information that contains additional knowledge about a death time  of an insured.
Revised: In this paper we consider a market model where there are two levels of information , the public information generated by the financial assets , and a larger flow of information that contains additional knowledge about a death time of an insured.
Edit intent: fluency
Original: In this paper we consider a market model where there are two levels of information , the public information generated by the financial assets  and a larger flow of information that contains additional knowledge about a death time  of an insured.
Revised: In this paper we consider a market model where there are two levels of information , the public information generated by the financial assets and a larger flow of information that contains additional knowledge about a death time (random time/horizon) of an insured.
Edit intent: meaning-changed
Original:  In this context, which catches real features such as correlation between  market model and  time of death, we address the risk-minimisation problem for a large class of equity-linked mortality and/or mortality contracts.
Revised:  In this context, which catches real features such as correlation between the market model and time of death, we address the risk-minimisation problem for a large class of equity-linked mortality and/or mortality contracts.
Edit intent: fluency
Original:  In this context, which catches real features such as correlation between  market model and  time of death, we address the risk-minimisation problem for a large class of equity-linked mortality and/or mortality contracts.
Revised:  In this context, which catches real features such as correlation between market model and the time of death, we address the risk-minimisation problem for a large class of equity-linked mortality and/or mortality contracts.
Edit intent: fluency
Original:  In this context, which catches real features such as correlation between  market model and  time of death, we address the risk-minimisation problem for a large class of equity-linked mortality and/or mortality contracts.
Revised:  In this context, which catches real features such as correlation between market model and time of death, we address the risk-minimization problem \`a la F\"ollmer-Sondermann for a large class of equity-linked mortality and/or mortality contracts.
Edit intent: meaning-changed
Original:  The stochastic innovation, that we propose herein, consists of singling out three classes of martingales in the large filtration. One of these classes is generated by a new process, up to our knowledge, that has nice features. The three orthogonal martingale classes are vital pillars for establishing our optional martingale representation theorem, when (local ) martingales of the large filtration are stopped at the death time  .
Revised:  The challenge in this setting, when no model specification for these securities nor for the death time is given, lies in finding the dynamics and the structures for the mortality/longevity securities used in the securitization. To overcome this obstacle, we elaborate our optional martingale representation theorem, when (local ) martingales of the large filtration are stopped at the death time .
Edit intent: coherence
Original:  The three orthogonal martingale classes are vital pillars for establishing our optional martingale representation theorem, when (local ) martingales of the large filtration are stopped at the death time  .
Revised:  The three orthogonal martingale classes are vital pillars for establishing our optional martingale representation theorem, when (local ) martingales of the large filtration are stopped at the death time can be decomposed into several and precise orthogonal local martingales .
Edit intent: meaning-changed
Original:  This constitutes our first main original contribution, while the second main contribution lies in describing, as explicit as possible, the optimal strategy when hedging mortalityrisks using the optional martingale representation .
Revised:  This constitutes our first principal novel contribution. Thanks to this optional representation, we succeed to decompose the risk in some popular mortality and/or longevity securities into the sum of orthogonal risks using a risk basis. One of the components of this basis is a new martingale, in the large filtration, that possesses nice features. Hence, the dynamics of mortality and longevity securities used in the securitization is described without mortality specification, and this constitutes our second novel contribution. Our third main contribution resides in finding explicitly the risk-minimization strategy as well as the corresponding undiversified risk for a largest class of mortality/longevity linked liabilities with or without the mortality securitization .
Edit intent: coherence
Original:   The result is an immediate consequence of a theorem by Rockafellar which states that every element of a linear subspace can be written as a conformal sum (a sum without cancelations) of elementary vectors (support-minimal vectors).
Revised:  However, only a decomposition without cancelations is biochemically meaningful, since a reversible reaction cannot have different directions in the contributing elementary modes. This essential requirement has been largely overlooked by the metabolic pathway community. Indeed, every flux mode can be decomposed into elementary modes without cancelations. The result is an immediate consequence of a theorem by Rockafellar which states that every element of a linear subspace can be written as a conformal sum (a sum without cancelations) of elementary vectors (support-minimal vectors).
Edit intent: meaning-changed
Original:   The result is an immediate consequence of a theorem by Rockafellar which states that every element of a linear subspace can be written as a conformal sum (a sum without cancelations) of elementary vectors (support-minimal vectors).
Revised:  The result is an immediate consequence of a theorem by Rockafellar which states that every element of a linear subspace is a conformal sum (a sum without cancelations) of elementary vectors (support-minimal vectors).
Edit intent: clarity
Original:  In this work, we extend the theorem to general polyhedral cones and polyhedra , thereby refining Minkowski's and Caratheodory 's theorems  in polyhedral geometry.
Revised:  In this work, we extend the theorem , first to "subspace cones" and then to general polyhedral cones and polyhedra , thereby refining Minkowski's and Caratheodory 's theorems in polyhedral geometry.
Edit intent: meaning-changed
Original:  In this work, we extend the theorem to general polyhedral cones and polyhedra , thereby refining Minkowski's and Caratheodory 's theorems  in polyhedral geometry.
Revised:  In this work, we extend the theorem to general polyhedral cones and polyhedra . Thereby, we refine Minkowski's and Caratheodory 's theorems in polyhedral geometry.
Edit intent: coherence
Original:  In this work, we extend the theorem to general polyhedral cones and polyhedra , thereby refining Minkowski's and Caratheodory 's theorems  in polyhedral geometry.
Revised:  In this work, we extend the theorem to general polyhedral cones and polyhedra , thereby refining Minkowski's and Carath\'eodory 's theorems in polyhedral geometry.
Edit intent: fluency
Original:  In this work, we extend the theorem to general polyhedral cones and polyhedra , thereby refining Minkowski's and Caratheodory 's theorems  in polyhedral geometry.
Revised:  In this work, we extend the theorem to general polyhedral cones and polyhedra , thereby refining Minkowski's and Caratheodory 's theorems , two fundamental results in polyhedral geometry.
Edit intent: meaning-changed
Original:  As an application, every flux mode can be decomposed into elementary modes without cancelations. Only such a decomposition is biochemically meaningful, in the sense that a reversible reaction cannot have different directions in the contributing elementary modes. We give elementary proofs for our mathematical results , in particular, we do not assume previous knowledge of polyhedral geometry.
Revised:  Our treatment is mathematically rigorous, but suitable for systems biologists, since we give self-contained proofs for our mathematical results , in particular, we do not assume previous knowledge of polyhedral geometry.
Edit intent: meaning-changed
Original:  We give elementary proofs for our mathematical results , in particular, we do not assume previous knowledge of polyhedral geometry. We define special cones arising from linear subspaces and nonnegativity conditions  and use them to analyze general polyhedral cones and polyhedra  .
Revised:  We give elementary proofs for our mathematical results , in particular, we study cones defined by linear subspaces and nonnegativity conditions and use them to analyze general polyhedral cones and polyhedra .
Edit intent: clarity
Original:  We define special cones arising from linear subspaces and nonnegativity conditions  and use them to analyze general polyhedral cones and polyhedra  .
Revised:  We define special cones arising from linear subspaces and nonnegativity conditions and use them to analyze general polyhedral cones and polyhedra . Finally, we review applications of elementary vectors and conformal sums in metabolic pathway analysis .
Edit intent: meaning-changed
Original:  We propose a new approach, using Chromatin feature Assortativity (ChAs), to integrate the epigenomic landscape of a specific cell type with its chromatin interaction network . Results: We use high-resolution Promoter Capture Hi-C and Hi-Cap data as well as ChIA-PET data from  embryonic stem cells to generate promoter-centered interaction networks.
Revised:  We propose a new approach, using chromatin assortativity to integrate the epigenomic landscape of a specific cell type with its chromatin interaction network . Results: We use high-resolution Promoter Capture Hi-C and Hi-Cap data as well as ChIA-PET data from embryonic stem cells to generate promoter-centered interaction networks.
Edit intent: clarity
Original:  We propose a new approach, using Chromatin feature Assortativity (ChAs), to integrate the epigenomic landscape of a specific cell type with its chromatin interaction network . Results: We use high-resolution Promoter Capture Hi-C and Hi-Cap data as well as ChIA-PET data from  embryonic stem cells to generate promoter-centered interaction networks.
Revised:  We propose a new approach, using Chromatin feature Assortativity (ChAs), to integrate the epigenomic landscape of a specific cell type with its chromatin interaction network and thus investigate which proteins or chromatin marks mediate genomic contacts. We use high-resolution Promoter Capture Hi-C and Hi-Cap data as well as ChIA-PET data from embryonic stem cells to generate promoter-centered interaction networks.
Edit intent: meaning-changed
Original:  We propose a new approach, using Chromatin feature Assortativity (ChAs), to integrate the epigenomic landscape of a specific cell type with its chromatin interaction network . Results: We use high-resolution Promoter Capture Hi-C and Hi-Cap data as well as ChIA-PET data from  embryonic stem cells to generate promoter-centered interaction networks.
Revised:  We propose a new approach, using Chromatin feature Assortativity (ChAs), to integrate the epigenomic landscape of a specific cell type with its chromatin interaction network . Results: We use high-resolution Promoter Capture Hi-C and Hi-Cap data as well as ChIA-PET data from mouse embryonic stem cells to generate promoter-centered interaction networks.
Edit intent: meaning-changed
Original:  We propose a new approach, using Chromatin feature Assortativity (ChAs), to integrate the epigenomic landscape of a specific cell type with its chromatin interaction network . Results: We use high-resolution Promoter Capture Hi-C and Hi-Cap data as well as ChIA-PET data from  embryonic stem cells to generate promoter-centered interaction networks.
Revised:  We propose a new approach, using Chromatin feature Assortativity (ChAs), to integrate the epigenomic landscape of a specific cell type with its chromatin interaction network . Results: We use high-resolution Promoter Capture Hi-C and Hi-Cap data as well as ChIA-PET data from embryonic stem cells to investigate promoter-centered interaction networks.
Edit intent: clarity
Original:  We propose a new approach, using Chromatin feature Assortativity (ChAs), to integrate the epigenomic landscape of a specific cell type with its chromatin interaction network . Results: We use high-resolution Promoter Capture Hi-C and Hi-Cap data as well as ChIA-PET data from  embryonic stem cells to generate promoter-centered interaction networks. We calculate the presence of a collection of 78 chromatin features in the chromatin fragments constituting the nodes of the network.
Revised:  We propose a new approach, using Chromatin feature Assortativity (ChAs), to integrate the epigenomic landscape of a specific cell type with its chromatin interaction network . Results: We use high-resolution Promoter Capture Hi-C and Hi-Cap data as well as ChIA-PET data from embryonic stem cells to generate promoter-centered chromatin interaction networks and calculate the presence of a collection of 78 chromatin features in the chromatin fragments constituting the nodes of the network.
Edit intent: coherence
Original:  Based on the ChAs of these epigenomic features calculated in 4 different interaction networks , we find Polycomb Group proteins and associated histone marks to play a prominent role. Remarkably, in promoter-centered networks, we observe higher ChAs of the actively elongating form of RNA Polymerase 2  compared to inactive forms  in interactions between promoters and other elements.
Revised:  Based on the ChAs of these epigenomic features calculated in 4 different interaction networks , we find Polycomb Group proteins and associated histone marks are the features with the highest chromatin assortativity in promoter-centred networks. We then ask which features distinguish contacts amongst promoters from contacts between promoters and other genomic elements. We observe higher chromatin assortativity of the actively elongating form of RNA Polymerase 2 compared to inactive forms in interactions between promoters and other elements.
Edit intent: meaning-changed
Original:  Remarkably, in promoter-centered networks, we observe higher ChAs of the actively elongating form of RNA Polymerase 2  compared to inactive forms  in interactions between promoters and other elements.
Revised:  Remarkably, in promoter-centered networks, we observe higher ChAs of the actively elongating form of RNA Polymerase 2 (RNAPII) compared to inactive forms in interactions between promoters and other elements.
Edit intent: meaning-changed
Original:  Remarkably, in promoter-centered networks, we observe higher ChAs of the actively elongating form of RNA Polymerase 2  compared to inactive forms  in interactions between promoters and other elements.
Revised:  Remarkably, in promoter-centered networks, we observe higher ChAs of the actively elongating form of RNA Polymerase 2 compared to inactive forms only in interactions between promoters and other elements.
Edit intent: meaning-changed
Original:  In large-scale systems there are several types of "noise " that can affect the performance of distributed machine learning algorithms : straggler nodes, system failures, or communication bottlenecks . Moreover, redundancy is abundant: a plethora of nodes, a lot of spare storage, etc .
Revised:  In large-scale systems there are several types of "noise " that can affect the performance of distributed machine learning algorithms : straggler nodes, system failures, or communication bottlenecks -- but there has been little interaction cutting across codes, machine learning, and distributed systems .
Edit intent: meaning-changed
Original:  For matrix multiplication, we use codes to leverage the plethora of nodes and alleviate the effects of stragglers. We show that if the number of  workers is n, and the runtime of each subtask has an exponential tail, the optimal coded matrix multiplication is \Theta(\log n) times faster than the uncoded matrix multiplication.
Revised:  For matrix multiplication, we use codes to alleviate the effect of stragglers, and show that if the number of workers is n, and the runtime of each subtask has an exponential tail, the optimal coded matrix multiplication is \Theta(\log n) times faster than the uncoded matrix multiplication.
Edit intent: clarity
Original:  We show that if the number of  workers is n, and the runtime of each subtask has an exponential tail, the optimal coded matrix multiplication is \Theta(\log n) times faster than the uncoded matrix multiplication.
Revised:  We show that if the number of homogeneous workers is n, and the runtime of each subtask has an exponential tail, the optimal coded matrix multiplication is \Theta(\log n) times faster than the uncoded matrix multiplication.
Edit intent: meaning-changed
Original:  We show that if the number of  workers is n, and the runtime of each subtask has an exponential tail, the optimal coded matrix multiplication is \Theta(\log n) times faster than the uncoded matrix multiplication. In data shuffling, we use codes to exploit the excess in storage and reduce communication bottlenecks .
Revised:  We show that if the number of workers is n, and the runtime of each subtask has an exponential tail, coded computation can speed up distributed matrix multiplication by a factor of \log n. For data shuffling, we use codes to exploit the excess in storage and reduce communication bottlenecks .
Edit intent: clarity
Original:  We show that when \alpha is the fraction of the data matrix that can be cached at each worker, and n is the number of workers, coded shuffling \emph{ reduces the communication cost by a factor \Theta(\alpha \gamma(n) ) compared to uncoded shuffling, where \gamma(n) is the ratio of the cost of unicasting n messages to n users to broadcasting a common message (of the same size) to n users.
Revised:  We show that when a constant fraction \alpha of the data matrix that can be cached at each worker, and n is the number of workers, coded shuffling \emph{ reduces the communication cost by a factor \Theta(\alpha \gamma(n) ) compared to uncoded shuffling, where \gamma(n) is the ratio of the cost of unicasting n messages to n users to broadcasting a common message (of the same size) to n users.
Edit intent: clarity
Original:  We show that when \alpha is the fraction of the data matrix that can be cached at each worker, and n is the number of workers, coded shuffling \emph{ reduces the communication cost by a factor \Theta(\alpha \gamma(n) ) compared to uncoded shuffling, where \gamma(n) is the ratio of the cost of unicasting n messages to n users to broadcasting a common message (of the same size) to n users.
Revised:  We show that when \alpha is the fraction of the data matrix can be cached at each worker, and n is the number of workers, coded shuffling \emph{ reduces the communication cost by a factor \Theta(\alpha \gamma(n) ) compared to uncoded shuffling, where \gamma(n) is the ratio of the cost of unicasting n messages to n users to broadcasting a common message (of the same size) to n users.
Edit intent: fluency
Original:  We show that when \alpha is the fraction of the data matrix that can be cached at each worker, and n is the number of workers, coded shuffling \emph{ reduces the communication cost by a factor \Theta(\alpha \gamma(n) ) compared to uncoded shuffling, where \gamma(n) is the ratio of the cost of unicasting n messages to n users to broadcasting a common message (of the same size) to n users.
Revised:  We show that when \alpha is the fraction of the data matrix that can be cached at each worker, and n is the number of workers, \emph{ reduces the communication cost by a factor \Theta(\alpha \gamma(n) ) compared to uncoded shuffling, where \gamma(n) is the ratio of the cost of unicasting n messages to n users to broadcasting a common message (of the same size) to n users.
Edit intent: clarity