wanyu/IteraTeR_full_sent huggingface dataset:
Original:  In an homogeneous scenario, we derive a performance bound for such metric, and we show how this bound relates to two fundamental parameters: the upload bandwidth available at each node, and the number of neighbors a node may deliver chunks to.
Revised:  In a homogeneous scenario, we derive a performance bound for such metric, and we show how this bound relates to two fundamental parameters: the upload bandwidth available at each node, and the number of neighbors a node may deliver chunks to.
Edit intent: fluency
Original:  In this bound, n-step Fibonacci sequences do emerge, and appear to set the fundamental laws that characterize the optimal operation of chunk-based systems . A further technical contribution of the paper is an advance in the theory of n-step Fibonacci sums for which a prior reference result was missing .
Revised:  In this bound, n-step Fibonacci sequences do emerge, and appear to set the fundamental laws that characterize the optimal operation of chunk-based systems .
Edit intent: coherence
Original:  We study four models including the variants of Frank, Gumbel , Clayton copulas and find that the non-exchangeable Gumbel copula describes the data distribution and correlation very accurately .
Revised:  We employ four models for the production copula, that is, trivariate versions of Frank, Gumbel , Clayton copulas and find that the non-exchangeable Gumbel copula describes the data distribution and correlation very accurately .
Edit intent: meaning-changed
Original:  Assuming the diffusion component of the process is non-degenerate and a mild assumption on the singularity of the Levy measure, this paper shows that the value function is smooth in the continuation region for problems with either finite or infinite variation jumps .
Revised:  Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the Levy measure, this paper shows that the value function is smooth in the continuation region for problems with either finite or infinite variation jumps .
Edit intent: fluency
Original:  Assuming the diffusion component of the process is non-degenerate and a mild assumption on the singularity of the Levy measure, this paper shows that the value function is smooth in the continuation region for problems with either finite or infinite variation jumps .
Revised:  Assuming the diffusion component of the process is non-degenerate and a mild assumption on the singularity of the L\'{e measure, this paper shows that the value function is smooth in the continuation region for problems with either finite or infinite variation jumps .
Edit intent: meaning-changed
Original:  Assuming the diffusion component of the process is non-degenerate and a mild assumption on the singularity of the Levy measure, this paper shows that the value function is smooth in the continuation region for problems with either finite or infinite variation jumps . Moreover , the smooth-fit property is shown via the global regularity of the value function .
Revised:  Assuming the diffusion component of the process is non-degenerate and a mild assumption on the singularity of the Levy measure, this paper shows that the value function of problems on an unbounded domain with infinite activity jumps is W^{2,1 , the smooth-fit property is shown via the global regularity of the value function .
Edit intent: meaning-changed
Original:  Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of  problems on an unbounded domain with infinite activity jumps is W^{2,1}_{p, loc} . As a result, the smooth-fit property holds and the value function is C^{2,1 .
Revised:  Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with infinite activity jumps is W^{2,1}_{p, loc} . As a result, the smooth-fit property holds and the value function is C^{2,1 .
Edit intent: meaning-changed
Original:  Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of  problems on an unbounded domain with infinite activity jumps is W^{2,1}_{p, loc} . As a result, the smooth-fit property holds and the value function is C^{2,1 .
Revised:  Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of problems on an unbounded domain with infinite activity jumps is W^{2,1}_{p, loc} .
Edit intent: coherence
Original:  Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with infinite activity jumps is W^{2,1}_{p, loc}  .
Revised:  Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with finite/infinite variation jumps is in W^{2,1}_{p, loc} .
Edit intent: meaning-changed
Original:  Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with infinite activity jumps is W^{2,1}_{p, loc}  .
Revised:  Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with infinite activity jumps is W^{2,1}_{p, loc} . As a consequence, the smooth-fit property holds .
Edit intent: meaning-changed
Original:  Assuming  the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with finite/infinite variation jumps is in W^{2,1}_{p, loc}  . As a consequence, the smooth-fit property holds.
Revised:  Assuming that the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with finite/infinite variation jumps is in W^{2,1}_{p, loc} . As a consequence, the smooth-fit property holds.
Edit intent: fluency
Original:  Assuming  the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with finite/infinite variation jumps is in W^{2,1}_{p, loc}  . As a consequence, the smooth-fit property holds.
Revised:  Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of this optimal stopping problem on an unbounded domain with finite/infinite variation jumps is in W^{2,1}_{p, loc} . As a consequence, the smooth-fit property holds.
Edit intent: meaning-changed
Original:  Assuming  the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with finite/infinite variation jumps is in W^{2,1}_{p, loc}  . As a consequence, the smooth-fit property holds.
Revised:  Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with finite/infinite variation jumps is in W^{2,1}_{p, loc} with p\in(1, \infty) . As a consequence, the smooth-fit property holds.
Edit intent: meaning-changed
Original:  In this manual , we describe how to use the software together with COMSOL Multiphysics 3.4 and Matlab to set up simulations. We provide a detailed account of the code structure and of the available interfaces. This makes modifications and extensions of the code possible. We also give two detailed examples, in which we describe the process of simulating and visualizing two models from the systems biology literature in a step-by-step manner .
Revised:  This manual describes version 1.1 of the software .
Edit intent: meaning-changed
Original:  This manual describes version 1.1 of the software  .
Revised:  This manual describes version 1.1 of the software . URDME 1.2 includes support for Comsol Multiphysics 4.1, 4.2, 4.3 as well as the previous version 3.5a. Additionally, support for basic SBML has been added along with the possibility to compile in stand-alone mode .
Edit intent: meaning-changed
Original:  URDME 1.2 includes support for Comsol Multiphysics 4.1, 4.2, 4.3 as well as the previous version 3.5a.
Revised:  URDME 1.3 includes support for Comsol Multiphysics 4.1, 4.2, 4.3 as well as the previous version 3.5a.
Edit intent: meaning-changed
Original:  URDME 1.2 includes support for Comsol Multiphysics 4.1, 4.2, 4.3 as well as the previous version 3.5a. Additionally, support for basic SBML has been added along with the possibility to compile in stand-alone mode .
Revised:  URDME 1.2 includes support for Comsol Multiphysics 5.x and PDE Toolbox version 1.5 and above .
Edit intent: meaning-changed
Original:  This incompatibility goes away by noticing that the model used in both approaches , geometric Brownian motion, is a non-ergodic process, in the sense that ensemble-average returns differ from time-average returns in a single realization .
Revised:  The conflict can be understood on the basis that the multiplicative models used in both approaches , geometric Brownian motion, is a non-ergodic process, in the sense that ensemble-average returns differ from time-average returns in a single realization .
Edit intent: meaning-changed
Original:  This incompatibility goes away by noticing that the model used in both approaches , geometric Brownian motion, is a non-ergodic process, in the sense that ensemble-average returns differ from time-average returns in a single realization .
Revised:  This incompatibility goes away by noticing that the model used in both approaches are non-ergodic process, in the sense that ensemble-average returns differ from time-average returns in a single realization .
Edit intent: clarity
Original:  This incompatibility goes away by noticing that the model used in both approaches , geometric Brownian motion, is a non-ergodic process, in the sense that ensemble-average returns differ from time-average returns in a single realization .
Revised:  This incompatibility goes away by noticing that the model used in both approaches , geometric Brownian motion, is a non-ergodic which leads to ensemble-average returns differ from time-average returns in a single realization .
Edit intent: clarity
Original:  This incompatibility goes away by noticing that the model used in both approaches , geometric Brownian motion, is a non-ergodic process, in the sense that ensemble-average returns differ from time-average returns in a single realization .
Revised:  This incompatibility goes away by noticing that the model used in both approaches , geometric Brownian motion, is a non-ergodic process, in the sense that ensemble-average returns differing from time-average returns in a single realization .
Edit intent: fluency
Original:  This incompatibility goes away by noticing that the model used in both approaches , geometric Brownian motion, is a non-ergodic process, in the sense that ensemble-average returns differ from time-average returns in a single realization .
Revised:  This incompatibility goes away by noticing that the model used in both approaches , geometric Brownian motion, is a non-ergodic process, in the sense that ensemble-average returns differ from time-average returns in single realizations .
Edit intent: fluency
Original:  The Kelly-result is obtained by considering  time-average returns. The averages differ by a logarithm. In portfolio theory this logarithm can be implemented as a logarithmic utility function. It is important to distinguish between effects of non-ergodicity and genuine utility constraints. For instance, ensemble-average returns depend linearly on leverage.
Revised:  The Kelly-result is obtained by considering time-average growth rates for an investment defines an optimal leverage, whereas growth rates derived from ensemble-average returns depend linearly on leverage.
Edit intent: meaning-changed
Original:  Our network modelis based on the distinct mechanochemical states of molecular motors. It can be regarded as a generalization of the one used by Steffen Liepelt and Reinhard Lipowsky (PRL 98, 258102 (2007)) . The method used in this research is similar as the one used by Michael E.
Revised:  The network model, a generalization of the one used by Steffen Liepelt and Reinhard Lipowsky (PRL 98, 258102 (2007)) . The method used in this research is similar as the one used by Michael E.
Edit intent: clarity
Original:  It can be regarded as a generalization of the one used by Steffen Liepelt and Reinhard Lipowsky (PRL 98, 258102 (2007)) . The method used in this research is similar as the one used by Michael E.
Revised:  It can be regarded as a generalization of the recently work of Liepelt and Lipowsky (PRL 98, 258102 (2007)) . The method used in this research is similar as the one used by Michael E.
Edit intent: clarity
Original:  It can be regarded as a generalization of the one used by Steffen Liepelt and Reinhard Lipowsky (PRL 98, 258102 (2007)) . The method used in this research is similar as the one used by Michael E. Fisher and Anatoly B. Kolomeisky (PNAS(2001) 98(14) P7748-7753) .
Revised:  It can be regarded as a generalization of the one used by Steffen Liepelt and Reinhard Lipowsky (PRL 98, 258102 (2007)) , is based on the discrete mechanochemical states of a molecular motor with multiple cycles. By generalizing the mathematical method developed by Fisher and Kolomeisky for single cycle motor (PNAS(2001) 98(14) P7748-7753) .
Edit intent: meaning-changed
Original:  Fisher and Anatoly B. Kolomeisky (PNAS(2001) 98(14) P7748-7753) . Generally, the formulation of the velocity of molecular motors can be obtained .
Revised:  Fisher and Anatoly B. Kolomeisky (PNAS(2001) 98(14) P7748-7753) , we are able to obtain an explicit formula for the velocity of a molecular motor .
Edit intent: clarity
Original:  In accordance with the standard model of LD formation, we assumed that neutral lipids oil-out between the membrane leaflets of the endoplasmic reticulum (ER), resulting in LDs that bud-off when a critical size is reached.
Revised:  In accordance with the prevailing model of LD formation, we assumed that neutral lipids oil-out between the membrane leaflets of the endoplasmic reticulum (ER), resulting in LDs that bud-off when a critical size is reached.
Edit intent: clarity
Original:  In accordance with the standard model of LD formation, we assumed that neutral lipids oil-out between the membrane leaflets of the endoplasmic reticulum (ER), resulting in LDs that bud-off when a critical size is reached.
Revised:  In accordance with the standard model of LD formation, we assumed that neutral lipids oil-out between the membrane leaflets of the endoplasmic reticulum (ER), resulting in LD that bud-off when a critical size is reached.
Edit intent: clarity
Original:  Relying on this mechanism, we have calculated the change in the elastic free energy of the membrane caused by nascent LDs. We found a gradual de-mixing of lipids in the membrane leaflet that goes along with an increase in surface curvature at the site of LD formation.
Revised:  Relying on this mechanism, we have calculated the change in the elastic free energy of the membrane caused by nascent LD. Based on this model calculation, we found a gradual de-mixing of lipids in the membrane leaflet that goes along with an increase in surface curvature at the site of LD formation.
Edit intent: clarity
Original:  As a result of de-mixing , the phospholipid monolayer was able to gain energy during LD growth . This suggested that the formation of curved interfaces , necessary for the creation of a lipid droplet, were driven or supported by the process of lipid de-mixing.
Revised:  As a result of de-mixing , the phospholipid monolayer was able to gain energy during LD growth , which suggested that the formation of curved interfaces , necessary for the creation of a lipid droplet, were driven or supported by the process of lipid de-mixing.
Edit intent: coherence
Original:  This suggested that the formation of curved interfaces , necessary for the creation of a lipid droplet, were driven or supported by the process of lipid de-mixing. In the case of Saccharomyces cerevisiae LDs eventually detached from the ER at a critical diameter of about 30-50 nm.
Revised:  This suggested that the formation of curved interfaces was supported by or even driven by lipid demixing. In addition, we show that demixing is thermodynamically necessary as LD cannot bud-off otherwise. In the case of Saccharomyces cerevisiae LDs eventually detached from the ER at a critical diameter of about 30-50 nm.
Edit intent: meaning-changed
Original:  In the case of Saccharomyces cerevisiae LDs eventually detached from the ER at a critical diameter of about 30-50 nm. We concluded that if the standard model of LD formation is valid, LD biogenesis is a two step process.
Revised:  In the case of Saccharomyces cerevisiae LDs eventually detached from the ER at a critical diameter of about 13 nm. This diameter is far below the experimentally determined size of typical yeast LD. Thus, we concluded that if the standard model of LD formation is valid, LD biogenesis is a two step process.
Edit intent: meaning-changed
Original:  Our model applies if the cell radius, R, is much smaller than the distance , R_{cs} , up to which carrier sensing is effective. The condition R_{cs} >> R is likely to hold in a dense deployment of Access Points (APs) where, for every client or station (STA), there is an AP very close to the STA such that the STA can associate with the AP at a high Physical (PHY) rate.
Revised:  Our model applies if the cell radius, R, is much smaller than the distance , R_{cs} . We argue that, the condition R_{cs} >> R is likely to hold in a dense deployment of Access Points (APs) where, for every client or station (STA), there is an AP very close to the STA such that the STA can associate with the AP at a high Physical (PHY) rate.
Edit intent: clarity
Original:  The condition R_{cs} >> R is likely to hold in a dense deployment of Access Points (APs) where, for every client or station (STA), there is an AP very close to the STA such that the STA can associate with the AP at a high Physical (PHY) rate.
Revised:  The condition R_{cs} >> R is likely to hold in a dense deployment of Access Points (APs) where, for every client or station (STA), there is an AP very close to the STA such that the STA can associate with the AP at a high physical rate.
Edit intent: clarity
Original:  Based on the insights provided by our analytical model, we also propose a simple decentralized algorithm which provides static channel assignments that are \textit{Nash equilibria in pure strategies for the objective of maximizing \textit{normalized network throughput in as many steps as there are channels.
Revised:  Based on the insights provided by our analytical model, we propose a simple decentralized algorithm which provides static channel assignments that are \textit{Nash equilibria in pure strategies for the objective of maximizing \textit{normalized network throughput in as many steps as there are channels.
Edit intent: clarity
Original:  Based on the insights provided by our analytical model, we also propose a simple decentralized algorithm which provides static channel assignments that are \textit{Nash equilibria in pure strategies for the objective of maximizing \textit{normalized network throughput in as many steps as there are channels.
Revised:  Based on the insights provided by our analytical model, we also propose a simple decentralized algorithm which provides static channel assignments that are \textit{Nash equilibria in pure strategies for the objective of maximizing \textit{normalized network throughput in as many steps as there are channels.
Edit intent: fluency
Original:  Based on the insights provided by our analytical model, we also propose a simple decentralized algorithm which provides static channel assignments that are \textit{Nash equilibria in pure strategies for the objective of maximizing \textit{normalized network throughput in as many steps as there are channels.
Revised:  Based on the insights provided by our analytical model, we also propose a simple decentralized algorithm which provides static channel assignments that are \textit{Nash equilibria in pure strategies for the objective of maximizing \textit{ in as many steps as there are channels.
Edit intent: meaning-changed
Original:  Based on the insights provided by our analytical model, we also propose a simple decentralized algorithm which provides static channel assignments that are \textit{Nash equilibria in pure strategies for the objective of maximizing \textit{normalized network throughput in as many steps as there are channels.
Revised:  Based on the insights provided by our analytical model, we also propose a simple decentralized algorithm which provides static channel assignments that are \textit{Nash equilibria in pure strategies for the objective of maximizing \textit{normalized network throughput normalized network throughput. Our channel assignment algorithm requires neither any explicit knowledge of the topology nor any message passing, and provides assignments in only as many steps as there are channels.
Edit intent: meaning-changed
Original:  Briefly, when we apply a classical nonlinear neural-network learning to a quantum linear Schr\"odinger equation, as a result we get a nonlinear Schr\"odinger equation (NLS), performing as a quantum stochastic filter.
Revised:  Briefly, when we apply a classical nonlinear neural-network learning to a linear quantum Schr\"odinger equation, as a result we get a nonlinear Schr\"odinger equation (NLS), performing as a quantum stochastic filter.
Edit intent: meaning-changed
Original: After reviewing the strengthened hypotheses of the Shannon-MacMillan-Breiman Theorem, versus the standard statement of the Noiseless Coding Theorem, we state and prove a similar result for relative information , otherwise known as information gain. If the gain results from receiving a side message, this gain, when averaged over the ensemble of possible side messages, is precisely the pragmatic information defined in Weinberger ( 2002 ).
Revised: This paper is part of an ongoing investigation of "pragmatic information", defined in Weinberger ( 2002 ).
Edit intent: clarity