wanyu/IteraTeR_full_sent huggingface dataset:
Original:  However, it requires solving a nonconvex optimization problem and its scalability to genome-scale modelshas not been demonstrated.
Revised:  However, it leads to nonconvex optimization problems, and existing tools cannot scale to realistically large metabolic models. Thus, constraint estimation is still used sparingly despite its benefits for modeling cell metabolism, which is important for developing novel antimicrobials against pathogens, discovering cancer drug targets, and producing value-added chemicals.
Edit intent: coherence
Original:  Here, we develop a new algorithm that extends existing approaches for de novo objective generation and solve it using the alternating direction method of multipliers (ADMM) . We demonstrate our approach on a genome-scale model and show that it identifies de novo objectives from measured fluxes with tunable sparsity .
Revised:  Here, we develop an approach to estimate constraint reactions from data that can scale to realistically large metabolic models. Previous tools have been used on problems having less than 70 biochemical reactions and 60 metabolites, which limits real-life-size applications. We perform extensive experiments using 70 large-scale metabolic network models for URLanisms (including bacteria, yeasts, and mammals) and show that it identifies de novo objectives from measured fluxes with tunable sparsity .
Edit intent: meaning-changed
Original:  Here, we develop a new algorithm that extends existing approaches for de novo objective generation and solve it using the alternating direction method of multipliers (ADMM) . We demonstrate our approach on a genome-scale model and show that it identifies de novo objectives from measured fluxes with tunable sparsity .
Revised:  Here, we develop a new algorithm that extends existing approaches for de novo objective generation and solve it using the alternating direction method of multipliers (ADMM) . We demonstrate our approach on a genome-scale model and show that our algorithm can recover cellular constraint reactions .
Edit intent: meaning-changed
Original:  The cellular goal (the optimization problem  the cell is trying to solve) can be challenging to define experimentally for URLanisms, including human or mammalian cells, which have complex metabolic capabilities and are not well understood.
Revised:  The cellular goal (the optimization problem that the cell is trying to solve) can be challenging to define experimentally for URLanisms, including human or mammalian cells, which have complex metabolic capabilities and are not well understood.
Edit intent: fluency
Original:  The cellular goal (the optimization problem  the cell is trying to solve) can be challenging to define experimentally for URLanisms, including human or mammalian cells, which have complex metabolic capabilities and are not well understood.
Revised:  The cellular goal (the optimization problem the cell is trying to solve) can be challenging to derive experimentally for URLanisms, including human or mammalian cells, which have complex metabolic capabilities and are not well understood.
Edit intent: clarity
Original:  Thus , constraint estimation is still used sparingly despite its benefits for modeling cell metabolism, which is important for developing novel antimicrobials against pathogens, discovering cancer drug targets, and producing value-added chemicals.
Revised:  Hence , constraint estimation is still used sparingly despite its benefits for modeling cell metabolism, which is important for developing novel antimicrobials against pathogens, discovering cancer drug targets, and producing value-added chemicals.
Edit intent: coherence
Original:  We perform extensive experiments using 70 large-scale metabolic network models for URLanisms (including bacteria, yeasts, and mammals) and show that our algorithm can recover cellular constraint reactions  .
Revised:  We perform extensive experiments using 70 large-scale metabolic network models for URLanisms (including bacteria, yeasts, and mammals) and show that our algorithm can recover cellular constraint reactions , even when some measurements are missing .
Edit intent: meaning-changed
Original: Existing methods that aim to automatically cluster data into physically meaningful subsets typically require assumptions regarding the number, size, or shape of the coherent subgroups. We present a new method, simultaneous Coherent Structure Coloring (sCSC), which accomplishes the task of unsupervised clustering without a priori guidance regarding the underlying structure of the data.
Revised: Existing methods that aim to automatically cluster data into physically meaningful subsets typically require assumptions regarding the number, size, or shape of the subgroups. Here, we present a new method, simultaneous Coherent Structure Coloring (sCSC), which accomplishes the task of unsupervised clustering without a priori guidance regarding the underlying structure of the data.
Edit intent: coherence
Original:  To illustrate the versatility of the method, we apply it to frontier physics problems at vastly different temporal and spatial scales: in a theoretical model of geophysical fluid dynamics, in laboratory measurements of vortex ring formation and entrainment, and in atomistic simulation of the Protein G system. The theoretical flow involves sparse sampling of non-equilibrium dynamics, where this new technique can find and characterize the structures that govern fluid transport using two orders of magnitude less data than required by existing methods. Application of the method to empirical measurements of vortex formation leads to the discovery of a well defined region in which vortex ring entrainment occurs, with potential implications ranging from flow control to cardiovascular diagnostics.
Revised:  sCSC performs a sequence of binary splittings on the dataset such that the most dissimilar data points are required to be in separate clusters. To achieve this, we obtain a set of orthogonal coordinates along which dissimilarity in the dataset is maximized from a generalized eigenvalue problem based on the pairwise dissimilarity between the data points to be clustered. This sequence of bifurcations produces a binary tree representation of the system, from which the number of clusters in the data and their interrelationships naturally emerge. To illustrate the effectiveness of the method to empirical measurements of vortex formation leads to the discovery of a well defined region in which vortex ring entrainment occurs, with potential implications ranging from flow control to cardiovascular diagnostics.
Edit intent: meaning-changed
Original:  Application of the method to empirical measurements of vortex formation leads to the discovery of a well defined region in which vortex ring entrainment occurs, with potential implications ranging from flow control to cardiovascular diagnostics. Finally, the protein folding example demonstrates a data-rich application governed by equilibrium dynamics, where the technique in this manuscript automatically discovers the hierarchy of distinct processes that govern protein folding and clusters protein configurations accordingly. We anticipate straightforward translation to many other fields where existing analysis tools , such as k-means and traditional hierarchical clustering, require ad hoc assumptions on the data structure or lack the interpretability of the present method .
Revised:  Application of the method in the absence of a priori assumptions we apply it to two exemplary problems in fluid dynamics. Then, we illustrate its capacity for interpretability using a high-dimensional protein folding simulation dataset. While we restrict our examples to dynamical physical systems in this work, we anticipate straightforward translation to many other fields where existing analysis tools , such as k-means and traditional hierarchical clustering, require ad hoc assumptions on the data structure or lack the interpretability of the present method .
Edit intent: clarity
Original:  We anticipate straightforward translation to many other fields where existing analysis tools , such as k-means and traditional hierarchical clustering, require ad hoc assumptions on the data structure or lack the interpretability of the present method .
Revised:  We anticipate straightforward translation to other fields where existing analysis tools , such as k-means and traditional hierarchical clustering, require ad hoc assumptions on the data structure or lack the interpretability of the present method .
Edit intent: clarity
Original:  We anticipate straightforward translation to many other fields where existing analysis tools , such as k-means and traditional hierarchical clustering, require ad hoc assumptions on the data structure or lack the interpretability of the present method .
Revised:  We anticipate straightforward translation to many other fields where existing analysis tools , such as k-means and traditional hierarchical clustering, require ad hoc assumptions on the data structure , lack the interpretability of the present method .
Edit intent: fluency
Original:  We anticipate straightforward translation to many other fields where existing analysis tools , such as k-means and traditional hierarchical clustering, require ad hoc assumptions on the data structure or lack the interpretability of the present method . The method is also potentially generalizable to fields where the underlying processes are less accessible, such as genomics and neuroscience.
Revised:  We anticipate straightforward translation to many other fields where existing analysis tools , such as k-means and traditional hierarchical clustering, require ad hoc assumptions on the data structure or lack the interpretability of the present method , or in which the underlying processes are less accessible, such as genomics and neuroscience.
Edit intent: coherence
Original:  Here, we present a new method, simultaneous Coherent Structure Coloring (sCSC), which accomplishes the task of unsupervised clustering without a priori guidance regarding the underlying structure of the data. sCSC performs a sequence of binary splittings on the dataset such that the most dissimilar data points are required to be in separate clusters.
Revised:  Here, we present a new method, simultaneous coherent structure coloring (sCSC), which accomplishes the task of unsupervised clustering without a priori guidance regarding the underlying structure of the data. sCSC performs a sequence of binary splittings on the dataset such that the most dissimilar data points are required to be in separate clusters.
Edit intent: fluency
Original:  Here, we propose a new approach  based on convex duality instead of martingale measures duality: our prices will be expressed using Fenchel conjugate and bi-conjugate.
Revised:  Here, we propose a new approach for estimating the super-replication cost based on convex duality instead of martingale measures duality: our prices will be expressed using Fenchel conjugate and bi-conjugate.
Edit intent: meaning-changed
Original:  We propose several characterizations of the (AIP ) condition and also study the relation with (NA) and a stronger notion of (AIP) linked to the no-free lunch condition. We show in a one step model that under (AIP) the super-hedging cost is just the payoff's concave envelop. In the multiple-period case, for a particular, but still general setup, we propose a recursive scheme for the computation of a the super-hedging cost of a convex option .
Revised:  We propose several characterizations of the (AIP ) condition and also study the relation with the classical notions of no-arbitrage .
Edit intent: clarity
Original:  While such systems have inspired a large amount of research into designing theoretical models of self-assembling systems, and even laboratory-based implementations of them, these artificial models and systems often tend to be lacking in one of the powerful features of natural systems (e.g. the assembly and folding of proteins),  the dynamic reconfigurability of structures.
Revised:  While such systems have inspired a large amount of research into designing theoretical models of self-assembling systems, and even laboratory-based implementations of them, these artificial models and systems often tend to be lacking in one of the powerful features of natural systems (e.g. the assembly and folding of proteins), namely the dynamic reconfigurability of structures.
Edit intent: coherence
Original:  In the FTAM, the individual components are 2-dimensional  tiles as in the aTAM, but in the FTAM, bonds between the edges of tiles can be flexible, allowing bonds to flex and entire structures to reconfigure, thus allowing 2-dimensional components to form 3-dimensional structures.
Revised:  In the FTAM, the individual components are 2-dimensional square tiles as in the aTAM, but in the FTAM, bonds between the edges of tiles can be flexible, allowing bonds to flex and entire structures to reconfigure, thus allowing 2-dimensional components to form 3-dimensional structures.
Edit intent: meaning-changed
Original:  We also show that with such power comes a heavy burden in terms of computational complexity of simulation and prediction by proving that  for important properties of FTAM systems, determining their existence is intractable, even for properties which are easily computed for systems in less dynamic models.
Revised:  We also show that with such power comes a heavy burden in terms of computational complexity of simulation and prediction by proving that , for important properties of FTAM systems, determining their existence is intractable, even for properties which are easily computed for systems in less dynamic models.
Edit intent: fluency
Original:  We prove existence of solutions to the corresponding conditional McKean--Vlasov equation  and we show that the pathwise realisation of the common noise can both trigger and prevent blow-ups.
Revised:  We prove existence of solutions to the corresponding conditional McKean--Vlasov equation , by realising them as suitable limit points of the finite-dimensional system, and we show that the pathwise realisation of the common noise can both trigger and prevent blow-ups.
Edit intent: meaning-changed
Original:  We prove existence of solutions to the corresponding conditional McKean--Vlasov equation, by realising them as suitable limit points of the finite-dimensional  system, and we show that the pathwise realisation of the common noise can both trigger and prevent blow-ups.
Revised:  We prove existence of solutions to the corresponding conditional McKean--Vlasov equation, by realising them as suitable limit points of the finite-dimensional particle system, and we show that the pathwise realisation of the common noise can both trigger and prevent blow-ups.
Edit intent: meaning-changed
Original:  Although the dynamics in the model are continuous, the  feedback effect can lead to jump discontinuities in the solutions, which we refer to as `blow-ups' . We prove existence of solutions to the corresponding conditional McKean--Vlasov equation, by realising them as suitable limit points of the finite-dimensional particle system , and we show that the pathwise realisation of the common noise can both trigger and prevent blow-ups .
Revised:  Although the dynamics in the model are continuous, the feedback effect can lead to `blow-up' phenomena whereby solutions develop jump-discontinuities. Our main results are twofold and concern the conditional McKean--Vlasov equation, by realising them as suitable limit points of the finite-dimensional particle system , and we show that the pathwise realisation of the common noise can both trigger and prevent blow-ups .
Edit intent: clarity
Original:  We prove existence of solutions to the corresponding conditional McKean--Vlasov equation, by realising them as suitable limit points of the finite-dimensional particle system , and we show that the pathwise realisation of the common noise can both trigger and prevent blow-ups .
Revised:  We prove existence of solutions to the corresponding conditional McKean--Vlasov formulation of the model. First and foremost, we show that there are global solutions to this McKean--Vlasov problem, which can be realised as limit points of the finite-dimensional particle system , and we show that the pathwise realisation of the common noise can both trigger and prevent blow-ups .
Edit intent: clarity
Original:  We prove existence of solutions to the corresponding conditional McKean--Vlasov equation, by realising them as suitable limit points of the finite-dimensional particle system , and we show that the pathwise realisation of the common noise can both trigger and prevent blow-ups .
Revised:  We prove existence of solutions to the corresponding conditional McKean--Vlasov equation, by realising them as suitable limit points of a motivating particle system with common noise. Furthermore, we derive results on the occurrence of blow-ups, thereby showing how these events can be triggered or prevented by the pathwise realisations of the common noise can both trigger and prevent blow-ups .
Edit intent: meaning-changed
Original:  We prove existence of solutions to the corresponding conditional McKean--Vlasov equation, by realising them as suitable limit points of the finite-dimensional particle system , and we show that the pathwise realisation of the common noise can both trigger and prevent blow-ups .
Revised:  We prove existence of solutions to the corresponding conditional McKean--Vlasov equation, by realising them as suitable limit points of the finite-dimensional particle system , and we show that the pathwise realisation of the common noise .
Edit intent: clarity
Original:  This zigzag Morse filtration generalizes the %DIFDELCMD < {\em %%% filtered Morse complex of Mischaikow and Nanda ~\mbox{%DIFAUXCMD MischaikowN13 , defined for standard persistence.
Revised:  This zigzag Morse filtration generalizes the %DIFDELCMD < {\em %%% filtered Morse complex of Mischaikow and Nanda , defined for standard persistence.
Edit intent: clarity
Original: The human brain is capable of diverse feats of intelligence. A particularly salient example is the ability to deduce structure from time-varying auditory and visual stimuli, enabling humans to master the rules of language and to build rich expectations of their physical environment. The broad relevance of this ability for human cognition motivates the need for a first-principles model explicating putative mechanisms. Here we propose a general framework for structural learningin the brain, composed of an evolving, high-dimensional dynamical system driven by external stimuli or internal processes. We operationalize the scenario in which humans learn the rules that generate a sequence of stimuli, rather than the exemplar stimuli themselves. We model external stimuli as seemingly disordered chaotic time series generated by complex dynamical systems; the underlying structure being deduced is then that of the corresponding chaotic attractor . This approach allows us to demonstrate and theoretically explain the emergence of five distinct phenomena reminiscent of cognitive functions:
Revised: Regardless of the marked differences between biological and artificial neural systems, one fundamental similarity is that they are essentially dynamical systems that can learn to imitate other dynamical systems, without knowing their governing equations. The brain is able to learn the dynamic nature of the physical world via experience; analogously, artificial neural systems can learn the long-term behavior of complex dynamical systems from data. Yet, precisely how this implicit learning occurs remains unknown. Here, we draw inspiration from human neuroscience and from reservoir computing to propose a first-principles framework explicating putative mechanisms of implicit learning. Specifically, we show that an arbitrary dynamical system implicitly learns other dynamical attractors by embedding them into its own phase space through invertible generalized synchronization. By sustaining the embedding through fine-tuned feedback loops, the arbitrary dynamical system can imitate the attractor dynamics it has learned. To evaluate the mechanism's relevance, we construct several distinct neural network models that adaptively learn and imitate multiple attractors. We observe and explain the emergence of five distinct phenomena reminiscent of cognitive functions:
Edit intent: meaning-changed
Original:  (i) learning the structure of a chaotic system purely from  time series, (ii) generating new streams of stimuli from a chaotic system, (iii) switching stream generation among multiple learned chaotic systems , either spontaneously or in response to external perturbations , (iv) inferring missing data from sparse observations of the chaotic system, and (v) deciphering superimposed input from different chaotic systems.
Revised:  (i) imitating a dynamical system purely from time series, (ii) generating new streams of stimuli from a chaotic system, (iii) switching stream generation among multiple learned chaotic systems , either spontaneously or in response to external perturbations , (iv) inferring missing data from sparse observations of the chaotic system, and (v) deciphering superimposed input from different chaotic systems.
Edit intent: clarity
Original:  (i) learning the structure of a chaotic system purely from  time series, (ii) generating new streams of stimuli from a chaotic system, (iii) switching stream generation among multiple learned chaotic systems , either spontaneously or in response to external perturbations , (iv) inferring missing data from sparse observations of the chaotic system, and (v) deciphering superimposed input from different chaotic systems.
Revised:  (i) learning the structure of a chaotic system purely from learning the time series, (ii) generating new streams of stimuli from a chaotic system, (iii) switching stream generation among multiple learned chaotic systems , either spontaneously or in response to external perturbations , (iv) inferring missing data from sparse observations of the chaotic system, and (v) deciphering superimposed input from different chaotic systems.
Edit intent: coherence
Original:  (i) learning the structure of a chaotic system purely from  time series, (ii) generating new streams of stimuli from a chaotic system, (iii) switching stream generation among multiple learned chaotic systems , either spontaneously or in response to external perturbations , (iv) inferring missing data from sparse observations of the chaotic system, and (v) deciphering superimposed input from different chaotic systems.
Revised:  (i) learning the structure of a chaotic system purely from time series, (ii) learning multiple attractors by a single system, (iii) switching stream generation among multiple learned chaotic systems , either spontaneously or in response to external perturbations , (iv) inferring missing data from sparse observations of the chaotic system, and (v) deciphering superimposed input from different chaotic systems.
Edit intent: meaning-changed
Original:  (i) learning the structure of a chaotic system purely from  time series, (ii) generating new streams of stimuli from a chaotic system, (iii) switching stream generation among multiple learned chaotic systems , either spontaneously or in response to external perturbations , (iv) inferring missing data from sparse observations of the chaotic system, and (v) deciphering superimposed input from different chaotic systems.
Revised:  (i) learning the structure of a chaotic system purely from time series, (ii) generating new streams of stimuli from a chaotic system, (iii) switching among the imitations of multiple attractors , either spontaneously or in response to external perturbations , (iv) inferring missing data from sparse observations of the chaotic system, and (v) deciphering superimposed input from different chaotic systems.
Edit intent: meaning-changed