wanyu/IteraTeR_full_sent huggingface dataset:
Original: A recent formulation of random-phase-approximation polymer theory for disordered protein phase separation is applied to investigate how the tendency for multiple chains of a protein to phase separate, as characterized by the critical temperature T^*_{\rm cr}, is related to the protein's single-chain average radius of gyration \langle R _g \rangle.
Revised: A recent formulation of random-phase-approximation polymer theory for disordered protein phase separation is applied to investigate how the tendency for multiple chains of a protein to phase separate, as characterized by the critical temperature T^*_{\rm cr}, is related to the protein's single-chain average radius of gyration \langle R _{\rm g \rangle.
Edit intent: fluency
Original:  For a set of thirty model sequences containing different permutations of an equal number of positively and negatively charged residues, we found a striking correlation T^*_{\rm cr}\sim \langle R _g \rangle^{- \nu } with \nu\approx 3.5-6.0 , indicating that electrostatic effects have similar impact in promoting single-chain conformational compactness and phase separation.
Revised:  For a set of sequences containing different permutations of an equal number of positively and negatively charged residues, we found a striking correlation T^*_{\rm cr}\sim \langle R _g \rangle^{- \nu } with \nu\approx 3.5-6.0 , indicating that electrostatic effects have similar impact in promoting single-chain conformational compactness and phase separation.
Edit intent: clarity
Original:  For a set of thirty model sequences containing different permutations of an equal number of positively and negatively charged residues, we found a striking correlation T^*_{\rm cr}\sim \langle R _g \rangle^{- \nu } with \nu\approx 3.5-6.0 , indicating that electrostatic effects have similar impact in promoting single-chain conformational compactness and phase separation.
Revised:  For a set of thirty model sequences containing different permutations of an equal number of positively and negatively charged residues, we found a striking correlation T^*_{\rm cr}\sim \langle R _{\rm g \rangle^{- \nu } with \nu\approx 3.5-6.0 , indicating that electrostatic effects have similar impact in promoting single-chain conformational compactness and phase separation.
Edit intent: fluency
Original:  For a set of thirty model sequences containing different permutations of an equal number of positively and negatively charged residues, we found a striking correlation T^*_{\rm cr}\sim \langle R _g \rangle^{- \nu } with \nu\approx 3.5-6.0 , indicating that electrostatic effects have similar impact in promoting single-chain conformational compactness and phase separation.
Revised:  For a set of thirty model sequences containing different permutations of an equal number of positively and negatively charged residues, we found a striking correlation T^*_{\rm cr}\sim \langle R _g \rangle^{- \gamma } with \nu\approx 3.5-6.0 , indicating that electrostatic effects have similar impact in promoting single-chain conformational compactness and phase separation.
Edit intent: meaning-changed
Original:  For a set of thirty model sequences containing different permutations of an equal number of positively and negatively charged residues, we found a striking correlation T^*_{\rm cr}\sim \langle R _g \rangle^{- \nu } with \nu\approx 3.5-6.0 , indicating that electrostatic effects have similar impact in promoting single-chain conformational compactness and phase separation.
Revised:  For a set of thirty model sequences containing different permutations of an equal number of positively and negatively charged residues, we found a striking correlation T^*_{\rm cr}\sim \langle R _g \rangle^{- \nu } with \gamma as large as \sim 6.0 , indicating that electrostatic effects have similar impact in promoting single-chain conformational compactness and phase separation.
Edit intent: clarity
Original:  For a set of thirty model sequences containing different permutations of an equal number of positively and negatively charged residues, we found a striking correlation T^*_{\rm cr}\sim \langle R _g \rangle^{- \nu } with \nu\approx 3.5-6.0 , indicating that electrostatic effects have similar impact in promoting single-chain conformational compactness and phase separation.
Revised:  For a set of thirty model sequences containing different permutations of an equal number of positively and negatively charged residues, we found a striking correlation T^*_{\rm cr}\sim \langle R _g \rangle^{- \nu } with \nu\approx 3.5-6.0 , indicating that electrostatic effects have similarly significant impact on promoting single-chain conformational compactness and phase separation.
Edit intent: clarity
Original: An important theoretical question that arises is to understand the trade-offs and fundamental limits on accuracy, speed, and dissipation (energy consumption) . Recent theoretical work suggests that it should always be possible to reduce the error of KPR-based mechanisms by waiting longer and /or consuming more energy. Surprisingly, we find that this is not the case and that there actually exists an optimal point in the speed-energy-accuracy plane for KPR and its generalizations .
Revised: An important theoretical question that arises is to understand the trade-offs and fundamental limits on accuracy, speed, and dissipation (energy consumption) in KPR and its generalization. Here, we revisit this question through numerical simulations where we simultaneously measure the speed, accuracy, and energy consumption of the KPR and adaptive sorting networks for different parameter choices. Our simulations highlight the existence of a 'feasible operating regime' in the speed-energy-accuracy plane for KPR and its generalizations .
Edit intent: clarity
Original:  Here we show using a generic birth-death model that despite being far from equilibrium, biochemical feedback near a bifurcation point exhibits the scaling exponents of the mean-field universality class .
Revised:  Here we show using a generic birth-death model that despite being far from equilibrium, biochemical feedback near a bifurcation point exhibits the scaling exponents of the Ising universality class in the mean-field limit .
Edit intent: meaning-changed
Original: Biochemical feedback leads to dynamical transitions between cellular states, reminiscent of phase transitions in statistical physics. Yet it is unknown whether cells exhibit the scaling properties associated with phase transitions, and if they do, to which universality class or classes they belong. Here we show using a generic birth-death model that biochemical feedback near a bifurcation point exhibits the scaling exponents of the Ising universality class in the mean-field limit.
Revised: Positive feedback in biochemical networks can lead to a bifurcation in state space. Universality implies that if molecules are well mixed, this bifurcation should exhibit the critical scaling behavior of the Ising universality class in the mean-field limit.
Edit intent: clarity
Original:  The theory allows us to calculate an effective order parameter, temperature, external field, and heat capacity from T cell fluorescence data without fitting.
Revised:  Making this statement quantitative requires the appropriate mapping between the biochemical parameters and the Ising parameters. Here we derive this mapping rigorously and uniquely for a broad class of stochastic birth-death models with feedback, and show that the expected static and dynamic critical exponents emerge. The generality of the mapping allows us to calculate an effective order parameter, temperature, external field, and heat capacity from T cell fluorescence data without fitting.
Edit intent: meaning-changed
Original:  The theory allows us to calculate an effective order parameter, temperature, external field, and heat capacity from T cell fluorescence data without fitting. Experiments agree with the scaling predictions, suggesting that this type of nonequilibrium criticality plays an important role in cell biology .
Revised:  The theory allows us to calculate an effective order parameter, temperature, external field, and heat capacity from T cell flow cytometry data without needing to know the underlying molecular details. We find that T cells obey critical scaling relations and exhibit critical slowing down, and that the heat capacity determines molecule number from fluorescence data. We demonstrate that critical scaling holds even as our system is driven out of its steady state, via the Kibble-Zurek mechanism for driven critical systems. Our approach places a ubiquitous biological mechanism into a known class of physical systems and is immediately applicable to other biological data .
Edit intent: meaning-changed
Original: Positive feedback in biochemical networks can lead to a bifurcation in state space. Universality implies that if molecules are well mixed, this bifurcation should exhibit the critical scaling behavior of the Ising universality class in the mean-field limit.
Revised: We make rigorous the notion of universality in well-mixed stochastic models of biochemical feedback, namely that they scale near their bifurcation point according to the exponents of the mean-field Ising universality class in the mean-field limit.
Edit intent: clarity
Original:  Universality implies that if molecules are well mixed, this bifurcation should exhibit the critical scaling behavior of the Ising universality class in the mean-field limit. Making this statement quantitative requires the appropriate mapping between the biochemical parameters and the Ising parameters. Here we derive this mapping rigorously and uniquely for a broad class of stochastic birth-death models with feedback, and show that the expected static and dynamic critical exponents emerge. The generality of the mapping allows us to extract the order parameter, effective temperature, magnetic field,  and heat capacity from T cell flow cytometry data without needing to know the underlying molecular details.
Revised:  Universality implies that if molecules are well mixed, this bifurcation should exhibit the critical scaling behavior of the Ising universality class . In doing so, we derive a mapping of the biochemical parameters to an effective temperature, magnetic field, and heat capacity from T cell flow cytometry data without needing to know the underlying molecular details.
Edit intent: clarity
Original:  We find that T cells obey critical scaling relations and exhibit critical slowing down, and that the heat capacity determines molecule number from fluorescence data. We demonstrate that critical scaling holds even as our system is driven out of its steady state, via the Kibble-Zurek mechanism for driven critical systems. Our approach places a ubiquitous biological mechanism into a known class of physical systems and is immediately applicable to other biological data .
Revised:  We find that T cells obey critical scaling relations and exhibit critical slowing down, and that the heat capacity determines molecule number from fluorescence intensity. We explain this result in terms of the underlying fluctuations and demonstrate the generality of our work .
Edit intent: meaning-changed
Original: We make rigorous the notion of universality in well-mixed stochastic models of biochemical feedback , namely that they scale near their bifurcation point according to the exponents of the mean-field Ising universality class.
Revised: We map a class of well-mixed stochastic models of biochemical feedback , namely that they scale near their bifurcation point according to the exponents of the mean-field Ising universality class.
Edit intent: clarity
Original: We make rigorous the notion of universality in well-mixed stochastic models of biochemical feedback , namely that they scale near their bifurcation point according to the exponents of the mean-field Ising universality class. In doing so, we derive a mapping of the biochemical parameters to an effective temperature, magnetic field, order parameter, and heat capacity .
Revised: We make rigorous the notion of universality in well-mixed stochastic models of biochemical feedback , namely that they scale near their bifurcation point according to the exponents of the mean-field Ising model near the critical point. The mapping provides an effective temperature, magnetic field, order parameter, and heat capacity .
Edit intent: meaning-changed
Original:  In doing so, we derive a mapping of the biochemical parameters to an effective temperature, magnetic field, order parameter, and heat capacity . These effective thermodynamic quantities can be extracted from biological data without fitting or knowledge of the underlying molecular details.
Revised:  In doing so, we derive a mapping of the biochemical parameters to an effective temperature, magnetic field, order parameter, and heat capacity that can be extracted from biological data without fitting or knowledge of the underlying molecular details.
Edit intent: clarity
Original:  We demonstrate this procedure on fluorescence data from mouse T cells and interpret the findings. In the process, we discover an unanticipated result: the heat capacity allows inference of absolute molecule number from fluorescence intensity.
Revised:  We demonstrate this procedure on fluorescence data from mouse T cells , which reveals distinctions between how the cells respond to different drugs. We also show that the heat capacity allows inference of absolute molecule number from fluorescence intensity.
Edit intent: meaning-changed
Original:  We present a 2HAM system that strictly self-assembles the discrete Sierpinski's carpet with scale factor 1. Moreover, the 2HAM system that we give lends itself to being generalized and we describe how this system can be modified to obtain a 2HAM system that strictly self-assembles one of any fractal from an infinite set of fractals which we call 4-sided fractals.
Revised:  We present a 2HAM system that finitely self-assembles the discrete Sierpinski's carpet with scale factor 1. Moreover, the 2HAM system that we give lends itself to being generalized and we describe how this system can be modified to obtain a 2HAM system that strictly self-assembles one of any fractal from an infinite set of fractals which we call 4-sided fractals.
Edit intent: meaning-changed
Original:  We present a 2HAM system that strictly self-assembles the discrete Sierpinski's carpet with scale factor 1. Moreover, the 2HAM system that we give lends itself to being generalized and we describe how this system can be modified to obtain a 2HAM system that strictly self-assembles one of any fractal from an infinite set of fractals which we call 4-sided fractals.
Revised:  We present a 2HAM system that strictly self-assembles the discrete Sierpi\'nski carpet with scale factor 1. Moreover, the 2HAM system that we give lends itself to being generalized and we describe how this system can be modified to obtain a 2HAM system that strictly self-assembles one of any fractal from an infinite set of fractals which we call 4-sided fractals.
Edit intent: fluency
Original:  We present a 2HAM system that strictly self-assembles the discrete Sierpinski's carpet with scale factor 1. Moreover, the 2HAM system that we give lends itself to being generalized and we describe how this system can be modified to obtain a 2HAM system that strictly self-assembles one of any fractal from an infinite set of fractals which we call 4-sided fractals.
Revised:  We present a 2HAM system that strictly self-assembles the discrete Sierpinski's carpet with scale factor 1. Moreover, the 2HAM system that we give lends itself to being generalized and we describe how this system can be modified to obtain a 2HAM system that finitely self-assembles one of any fractal from an infinite set of fractals which we call 4-sided fractals.
Edit intent: meaning-changed
Original:  The 2HAM systems we give in this paper are the first examples of systems that strictly self-assemble discrete self-similar fractals at scale factor 1 in a purely growth model of self-assembly.
Revised:  The 2HAM systems we give in this paper are the first examples of systems that finitely self-assemble discrete self-similar fractals at scale factor 1 in a purely growth model of self-assembly.
Edit intent: meaning-changed
Original:  The dual-sparsity based non-rigid registration model is enhanced with a reweighting scheme, and solved by transferring the model into some alternating optimized subproblems which have exact solutions and guaranteed convergence.
Revised:  The double sparsity based non-rigid registration model is enhanced with a reweighting scheme, and solved by transferring the model into some alternating optimized subproblems which have exact solutions and guaranteed convergence.
Edit intent: fluency
Original:  The dual-sparsity based non-rigid registration model is enhanced with a reweighting scheme, and solved by transferring the model into some alternating optimized subproblems which have exact solutions and guaranteed convergence.
Revised:  The dual-sparsity based non-rigid registration model is enhanced with a reweighting scheme, and solved by transferring the model into four alternately-optimized subproblems which have exact solutions and guaranteed convergence.
Edit intent: meaning-changed
Original:  We present an exact algorithm solving the problem in O(n \log ^4 n) time and a (1+\varepsilon)-approximation algorithm running in O(n + 1/\varepsilon^2\cdot\log ^4 (1/\varepsilon)) time.
Revised:  We present an exact algorithm solving the problem in O(n \log ^2 n) time and a (1+\varepsilon)-approximation algorithm running in O(n + 1/\varepsilon^2\cdot\log ^4 (1/\varepsilon)) time.
Edit intent: meaning-changed
Original:  We present an exact algorithm solving the problem in O(n \log ^4 n) time and a (1+\varepsilon)-approximation algorithm running in O(n + 1/\varepsilon^2\cdot\log ^4 (1/\varepsilon)) time.
Revised:  We present an exact algorithm solving the problem in O(n \log ^4 n) time and a (1+\varepsilon)-approximation algorithm running in O(n + 1/\varepsilon^2\cdot\log ^2 (1/\varepsilon)) time.
Edit intent: fluency
Original:  To do so, a model for the market dynamicsis needed. While the traditional replication or superreplication strategies find the optimal prices under the constraint that all risks are shifted to the counterparty, we weaken this assumption here by introducing risk (resp. acceptability) functionals in the stochastic optimizationframework. Moreover, we consider the associated ambiguity problem, where we replace the single probability model by a non-parametric set of models .
Revised:  To do so, a model for the underlying asset price dynamics .
Edit intent: clarity
Original:  We show that weakening the acceptability constraint leads to a shrinking bid-ask spread while considering model ambiguity makes the bid-ask spread even larger. Some algorithms and numerical examples are presented .
Revised:  Given this model, optimal bid and ask prices can be found by stochastic optimization. However, the model for the underlying asset price process is typically based on data and found by a nonparametric statistical estimation procedure. We define a confidence set of possible estimated models by a nonparametric neighborhood of a baseline model. This neighborhood serves as ambiguity set for a stochastic optimization problem under model uncertainty. We obtain distributionally robust solutions of the acceptability pricing problem and derive the dual problem formulation. Moreover, we relate the bid and ask prices under model ambiguity to the quality of the observed data .
Edit intent: meaning-changed
Original:  we reveal a quantitative relation between stochastic fluctuations and feedback regulation at the single-molecule level, which provides novel insights into how and to what extent a feedback loop can enhance or suppress molecular fluctuations ] . Based on such relation, we also develop an effective method to extract the topological information of gene regulatory networks from single-cell gene expression data  .
Revised:  we reveal a quantitative relation between stochastic fluctuations and feedback topology, perfecting the results in ] . Based on such relation, we also develop an effective method to extract the topological information of gene regulatory networks from single-cell gene expression data .
Edit intent: meaning-changed
Original:  we reveal a quantitative relation between stochastic fluctuations and feedback regulation at the single-molecule level, which provides novel insights into how and to what extent a feedback loop can enhance or suppress molecular fluctuations ] . Based on such relation, we also develop an effective method to extract the topological information of gene regulatory networks from single-cell gene expression data  .
Revised:  we reveal a quantitative relation between stochastic fluctuations and feedback regulation at the single-molecule level, which provides novel insights into how and to what extent a feedback loop can enhance or suppress molecular fluctuations Phys. Rev. Lett. 113:268105, 2014] . Based on such relation, we also develop an effective method to extract the topological information of gene regulatory networks from single-cell gene expression data .
Edit intent: meaning-changed
Original:  we reveal a quantitative relation between stochastic fluctuations and feedback regulation at the single-molecule level, which provides novel insights into how and to what extent a feedback loop can enhance or suppress molecular fluctuations ] . Based on such relation, we also develop an effective method to extract the topological information of gene regulatory networks from single-cell gene expression data  .
Revised:  we reveal a quantitative relation between stochastic fluctuations and feedback regulation at the single-molecule level, which provides novel insights into how and to what extent a feedback loop can enhance or suppress molecular fluctuations ]. In negative-feedback networks, we find a fundamental inequality similar to the Carnot theorem in classical thermodynamics . Based on such relation, we also develop an effective method to extract the topological information of gene regulatory networks from single-cell gene expression data .
Edit intent: meaning-changed
Original:  we reveal a quantitative relation between stochastic fluctuations and feedback regulation at the single-molecule level, which provides novel insights into how and to what extent a feedback loop can enhance or suppress molecular fluctuations ] . Based on such relation, we also develop an effective method to extract the topological information of gene regulatory networks from single-cell gene expression data  .
Revised:  we reveal a quantitative relation between stochastic fluctuations and feedback regulation at the single-molecule level, which provides novel insights into how and to what extent a feedback loop can enhance or suppress molecular fluctuations ] . Based on the fluctuation-feedback relation, we also develop an effective method to extract the topological information of gene regulatory networks from single-cell gene expression data .
Edit intent: clarity
Original:  we reveal a quantitative relation between stochastic fluctuations and feedback regulation at the single-molecule level, which provides novel insights into how and to what extent a feedback loop can enhance or suppress molecular fluctuations ] . Based on such relation, we also develop an effective method to extract the topological information of gene regulatory networks from single-cell gene expression data  .
Revised:  we reveal a quantitative relation between stochastic fluctuations and feedback regulation at the single-molecule level, which provides novel insights into how and to what extent a feedback loop can enhance or suppress molecular fluctuations ] . Based on such relation, we also develop an effective method to extract the topological information of a gene regulatory network from single-cell gene expression data .
Edit intent: fluency