wanyu/IteraTeR_v2 huggingface dataset:
Original:  Yet the discrete metric structure of shortest path lengths in a network , known as chemical distances, is definitely not the only reservoir of geometric distances that characterize many networks.
Revised:  Yet the geometry induced by shortest path distances in a network , known as chemical distances, is definitely not the only reservoir of geometric distances that characterize many networks.
Edit intent: clarity
Original:  Yet the discrete metric structure of shortest path lengths in a network , known as chemical distances, is definitely not the only reservoir of geometric distances that characterize many networks.
Revised:  Yet the discrete metric structure of shortest path lengths in a network is definitely not the only reservoir of geometric distances that characterize many networks.
Edit intent: clarity
Original:  The other forms of network-related geometries are the geometry of continuous latent spaces underlying many networks, and the effective geometry induced by dynamical processes in networks.
Revised:  The other forms of network-related geometries are the geometry of latent spaces underlying many networks, and the effective geometry induced by dynamical processes in networks.
Edit intent: clarity
Original:  Here, we review the most important theoretical and practical developments in network geometry in the last two decades, and offer perspectives on future research directions and challenges in this novel frontier in the study of complexity.
Revised:  Here, we review the most important theoretical and practical developments dealing with these approaches to network geometry in the last two decades, and offer perspectives on future research directions and challenges in this novel frontier in the study of complexity.
Edit intent: clarity
Original: Traffic in enterprise networks typically traverses a sequence of middleboxes forming a service function chain, or simply a chain.
Revised: Enterprise network traffic typically traverses a sequence of middleboxes forming a service function chain, or simply a chain.
Edit intent: clarity
Original:  The ability to tolerate failures when they occur along chains is imperative to the availability and reliability of enterprise applications.
Revised:  Tolerating failures when they occur along chains is imperative to the availability and reliability of enterprise applications.
Edit intent: clarity
Original:  Service outages due to chain failures severely impact customers and cause significant financial losses.
Edit intent: coherence
Original:  Making a chain fault-tolerant is challenging since, in the case of failures, the state of faulty middleboxes must be correctly and quickly recovered while providing high throughput and low latency.
Revised:  Making a chain fault-tolerant is challenging since, in the event of failures, the state of faulty middleboxes must be correctly and quickly recovered while providing high throughput and low latency.
Edit intent: fluency
Original:  In this paper, we present FTC, a novel system design and protocol for fault-tolerant service function chaining.
Revised:  In this paper, we introduce FTC, novel system design and protocol for fault-tolerant service function chaining.
Edit intent: coherence
Original:  In FTC, state updates caused by packet processing at a middlebox are collected, piggybacked onto the packet, and sent along the chain to be replicated.
Revised:  In FTC, state updates caused by packet processing at a middlebox are collected, piggybacked into the packet, and sent along the chain to be replicated.
Edit intent: clarity
Original: An orientation of an undirected graph G is an assignment of exactly one direction to each edge of G. An orientation of a graph G is called a strong orientation, if from each vertex there is a directed path to every other vertex.
Revised: An orientation of an undirected graph G is an assignment of exactly one direction to each edge of G. 
Edit intent: clarity
Original:  The oriented diameter of a graph G is the smallest diameter among all the strong orientations of G. The maximum oriented diameter of a family of graphs F is the maximum oriented diameter among all the graphs in F.
Revised:  The oriented diameter of a graph G is the smallest diameter among all the orientations of G. The maximum oriented diameter of a family of graphs F is the maximum oriented diameter among all the graphs in F.
Edit intent: clarity
Original: Here, we propose a class of scale-free networked graphs G(t;
Revised: Here, we propose a class of scale-free networks G(t;
Edit intent: clarity
Original:  average degrees \langle k\rangle of all the generated graphs are no longer a constant in the limit of large graph size, implying that they are not sparse but dense, (ii) power-law parameters \gamma of these models are precisely calculated equal to 2, as well (iii) their diameters D are all an invariant in the growth process of models.
Revised:  average degrees \langle k\rangle of all the generated networks are no longer a constant in the limit of large graph size, implying that they are not sparse but dense, (ii) power-law parameters \gamma of these models are precisely calculated equal to 2, as well (iii) their diameters D are all an invariant in the growth process of models.
Edit intent: clarity
Original:  average degrees \langle k\rangle of all the generated graphs are no longer a constant in the limit of large graph size, implying that they are not sparse but dense, (ii) power-law parameters \gamma of these models are precisely calculated equal to 2, as well (iii) their diameters D are all an invariant in the growth process of models.
Revised:  average degrees \langle k\rangle of all the generated graphs are no longer a constant in the limit of large graph size, implying that they are not sparse but dense, (ii) power-law parameters \gamma of these networks are precisely calculated equal to 2, as well (iii) their diameters D are all an invariant in the growth process of models.
Edit intent: clarity
Original:  While our models have deterministic structure with clustering coefficients equivalent to zero, we might be able to obtain various candidates with nonzero clustering coefficient based on original graphs using some reasonable approaches, for instance, randomly adding some new edges under the premise of keeping the three important properties above unchanged.
Revised:  While our models have deterministic structure with clustering coefficients equivalent to zero, we might be able to obtain various candidates with nonzero clustering coefficient based on original networks using some reasonable approaches, for instance, randomly adding some new edges under the premise of keeping the three important properties above unchanged.
Edit intent: clarity
Original:  In addition, we study trapping problem on graphs G(t;m) and then obtain closed-form solutions%DIFDELCMD < \langle %%% HT%DIFDELCMD < \rangle%%% _{t to mean hitting time \langle }\rangle .
Revised:  In addition, we study trapping problem on graphs G(t;m) and then obtain closed-form %DIFDELCMD < \langle %%% HT%DIFDELCMD < \rangle%%% _{t to mean hitting time \langle }\rangle .
Edit intent: clarity
Original:  In addition, we study trapping problem on graphs G(t;m) and then obtain closed-form solutions%DIFDELCMD < \langle %%% HT%DIFDELCMD < \rangle%%% _{t to mean hitting time \langle }\rangle .
Revised:  In addition, we study trapping problem on graphs G(t;m) and then obtain closed-form solutions%DIFDELCMD < \langle %%% %DIFDELCMD < \rangle%%% _{t to mean hitting time \langle }\rangle .
Edit intent: coherence
Original:  In addition, we study trapping problem on graphs G(t;m) and then obtain closed-form solutions%DIFDELCMD < \langle %%% HT%DIFDELCMD < \rangle%%% _{t to mean hitting time \langle }\rangle .
Revised:  In addition, we study trapping problem on graphs G(t;m) and then obtain closed-form solutions%DIFDELCMD < \langle %%% HT%DIFDELCMD < \rangle%%% solution to mean hitting time \langle }\rangle .
Edit intent: fluency
Original:  As opposed to other  models, our results show an unexpected phenomenon that  \langle HT \rangle_{t} is approximately close to the logarithm of order of graphs G(t;m) however not to the order itself . From the theoretical point of view, these networked graphs considered here can be thought of as counterexamples for most of the published models obeying power-law distribution in current study.
Revised:  As opposed to other previous models, our results show an unexpected phenomenon that \langle HT \rangle_{t} is approximately close to the logarithm of order of graphs G(t;m) however not to the order itself . From the theoretical point of view, these networked graphs considered here can be thought of as counterexamples for most of the published models obeying power-law distribution in current study.
Edit intent: clarity
Original:  As opposed to other  models, our results show an unexpected phenomenon that  \langle HT \rangle_{t} is approximately close to the logarithm of order of graphs G(t;m) however not to the order itself . From the theoretical point of view, these networked graphs considered here can be thought of as counterexamples for most of the published models obeying power-law distribution in current study.
Revised:  As opposed to other models, our results show an unexpected phenomenon that \langle HT \rangle_{t} is approximately close to the logarithm of order of graphs G(t;m) . From the theoretical point of view, these networked graphs considered here can be thought of as counterexamples for most of the published models obeying power-law distribution in current study.
Edit intent: coherence
Original:  As opposed to other  models, our results show an unexpected phenomenon that  \langle HT \rangle_{t} is approximately close to the logarithm of order of graphs G(t;m) however not to the order itself . From the theoretical point of view, these networked graphs considered here can be thought of as counterexamples for most of the published models obeying power-law distribution in current study.
Revised:  As opposed to other models, our results show an unexpected phenomenon that \langle HT \rangle_{t} is approximately close to the logarithm of order of graphs G(t;m) however not to the order itself . From the theoretical point of view, these networked models considered here can be thought of as counterexamples for most of the published models obeying power-law distribution in current study.
Edit intent: fluency
Original:  In this article we  analyse the statistical properties of the Bayesian estimator for the selection coefficient in this model , when both selection and mutation are acting on the population.
Revised:  In this article we analyse the statistical properties of the Bayesian estimator for the selection parameter , when both selection and mutation are acting on the population.
Edit intent: clarity
Original:  In particular, it is shown that this estimator is uniformly consistent over compact sets , uniformly asymptotically normal, and displays uniform convergence of moments on compact sets .
Revised:  In particular, it is shown that these estimators are uniformly over compact sets , uniformly asymptotically normal, and displays uniform convergence of moments on compact sets .
Edit intent: clarity
Original:  Most importantly, our inverse-PDE solver allows effortless integration of domain-specific knowledge about the physics of  underlying fields, such as symmetries and proper basis functions.
Revised:  Most importantly, our inverse-PDE solver enables effortless integration of domain-specific knowledge about the physics of underlying fields, such as symmetries and proper basis functions.
Edit intent: fluency
Original:  Most importantly, our inverse-PDE solver allows effortless integration of domain-specific knowledge about the physics of  underlying fields, such as symmetries and proper basis functions.
Revised:  Most importantly, our inverse-PDE solver allows effortless integration of domain-specific knowledge about the physics of the underlying fields, such as symmetries and proper basis functions.
Edit intent: fluency
Original:  We call this approach Blended Inverse-PDE Networks (hereby dubbed BIPDE-Nets ) and demonstrate its applicability on recovering the variable diffusion coefficient in Poisson problems in one and two spatial dimensions  .
Revised:  We call this architecture Blended inverse-PDE networks (hereby dubbed BIPDE-Nets ) and demonstrate its applicability on recovering the variable diffusion coefficient in Poisson problems in one and two spatial dimensions .
Edit intent: clarity
Original:  We call this approach Blended Inverse-PDE Networks (hereby dubbed BIPDE-Nets ) and demonstrate its applicability on recovering the variable diffusion coefficient in Poisson problems in one and two spatial dimensions  .
Revised:  We call this approach Blended Inverse-PDE Networks (hereby dubbed BiPDE networks ) and demonstrate its applicability on recovering the variable diffusion coefficient in Poisson problems in one and two spatial dimensions .
Edit intent: clarity
Original: We propose a novel composite framework that enables finding unknown fields in the context of inverse problems for partial differential equations (PDEs).
Revised: We propose a novel composite framework to find unknown fields in the context of inverse problems for partial differential equations (PDEs).
Edit intent: clarity
Original:  Our design brings together techniques of computational mathematics, machine learning and pattern recognition under one umbrella to seamlessly incorporate any domain-specific knowledge and insights through modeling .
Revised:  Our design brings together techniques of computational mathematics, machine learning and pattern recognition under one umbrella to incorporate domain-specific knowledge and insights through modeling .
Edit intent: clarity
Original:  The network is explicitly aware of the governing physics through a hard-coded PDE solver layer in contrast to  existing methods that incorporate the governing equations in the loss function ;
Revised:  The network is explicitly aware of the governing physics through a hard-coded PDE solver layer in contrast to most existing methods that incorporate the governing equations in the loss function ;
Edit intent: clarity
Original:  We call this architecture Blended inverse-PDE networks (hereby dubbed BiPDE networks) and demonstrate its applicability on recovering the variable diffusion coefficient in Poisson problems in one and two spatial dimensions, as well as the diffusion coefficient in the time-dependent and nonlinear Burgers' equation in one dimension.
Revised:  We call this architecture Blended inverse-PDE networks (hereby dubbed BiPDE networks) and demonstrate its applicability for recovering the variable diffusion coefficient in Poisson problems in one and two spatial dimensions, as well as the diffusion coefficient in the time-dependent and nonlinear Burgers' equation in one dimension.
Edit intent: clarity
Original: The emergence of generative models based on deep neural networks has recently enabled the automatic generation of massive amounts of graphical content, both in 2D and in 3D.
Revised: The emergence of deep generative models has recently enabled the automatic generation of massive amounts of graphical content, both in 2D and in 3D.
Edit intent: clarity
Original:  In such cases, reshaping a uniform or normal distribution over the latent space into a complex multi-modal distribution in the data domain is challenging, and the quality of the generated samples may suffer as a result .
Revised:  In such cases, reshaping a uniform or normal distribution over the latent space into a complex multi-modal distribution in the data domain is challenging, and the generator might fail to sample the target distribution well .
Edit intent: clarity
Original:  Furthermore, the different modes are entangled with the other attributes of the data, and thus, mode transitions cannot be well controlled via continuous style parameters .
Revised:  Furthermore, existing unsupervised generative models are not able to control the mode of the generated samples independently of the other visual attributes, despite the fact that they are typically disentangled in the training data .
Edit intent: clarity
Original:  In this paper, we introduce uMM-GAN , a novel architecture designed to better model such multi-modal distributions, in an unsupervised fashion.
Revised:  In this paper, we introduce UMMGAN , a novel architecture designed to better model such multi-modal distributions, in an unsupervised fashion.
Edit intent: fluency
Original:  In this paper, we introduce uMM-GAN , a novel architecture designed to better model such multi-modal distributions, in an unsupervised fashion.
Revised:  In this paper, we introduce uMM-GAN , a novel architecture designed to better model multi-modal distributions, in an unsupervised fashion.
Edit intent: clarity
Original:  Quite strikingly, we show that this approach is capable of homing onto the natural modes in the training set, and effectively approximates the complex distribution as a superposition of multiple simple ones.
Revised:  We demonstrate that this approach is capable of homing onto the natural modes in the training set, and effectively approximates the complex distribution as a superposition of multiple simple ones.
Edit intent: coherence
Original:  Quite strikingly, we show that this approach is capable of homing onto the natural modes in the training set, and effectively approximates the complex distribution as a superposition of multiple simple ones.
Revised:  Quite strikingly, we show that this approach is capable of effectively approximating a complex distribution as a superposition of multiple simple ones.
Edit intent: coherence
Original:  We demonstrate that uMM-GAN copes better with multi-modal distributions, while at the same time disentangling between the modes and their style, thereby providing an independent degree of control over the generated content.
Revised:  We further show that UMMGAN effectively disentangles between modes and style, thereby providing an independent degree of control over the generated content.
Edit intent: clarity
Original:  Polynomial Modular Number System (PMNS) is a convenient number system for modular arithmetic, introduced in 2004.
Revised:  Polynomial Modular Number Systems (PMNS) is a convenient number system for modular arithmetic, introduced in 2004.
Edit intent: fluency
Original:  And in turn, this also gives us the possibility to mine some information from such agents , such as the relationships between them, by the interactions in a game process.
Revised:  And in turn, this also gives us the opportunity to mine such information from agents by the observed interactions of them in a game process.
Edit intent: clarity
Original:  We apply GGN to the team game as a concrete application and conduct experiments on relationship inference tasks .
Revised:  We illustrate how to apply GGNs to infer the hidden relationships between agents with game behaviors and conduct experiments on relationship inference tasks .
Edit intent: clarity
Original:  Our framework can also be used for understanding dFNs in brain function in health and other neurological disorders  .
Revised:  Our framework can also be used for understanding dFNs in healthy brain function and in other neurological disorders .
Edit intent: clarity
Original:  Using confocal three-dimensional imaging, we find that motile rod-shaped M. xanthus cells are densely packed and aligned in each layer, forming an active nematic liquid crystal.
Revised:  Using confocal three-dimensional imaging, we find that motile rod-shaped M. xanthus cells are densely packed and aligned in each layer, forming an active nematic liquid crystal.
Edit intent: fluency
Original:  Our results suggest that cell motility and mechanical cell-cell interactions are sufficient to induce the formation of cell layers at topological defects, thereby seeding fruiting bodies in colonies of \textit{M. xanthus .
Revised:  Our results suggest that cell motility and mechanical cell-cell interactions are sufficient to induce the formation of cell layers at topological defects, thereby seeding fruiting bodies in colonies of \textit{M. xanthus .
Edit intent: fluency
Original:  We observe that new cell layers preferentially form at the position of +1/2 defects, whereas holes  open at -1/2 defects.
Revised:  We observe that new cell layers preferentially form at the position of +1/2 defects, whereas holes preferentially open at -1/2 defects.
Edit intent: coherence
Original:  Our results suggest that cell motility and mechanical cell-cell interactions are sufficient to induce the formation of cell layers at topological defects, thereby seeding fruiting bodies in colonies of M. xanthus.
Revised:  Our results suggest that cell motility and mechanical cell-cell interactions are sufficient to promote the formation of cell layers at topological defects, thereby seeding fruiting bodies in colonies of M. xanthus.
Edit intent: clarity
Original:  Relationships may fail, and given this idosyncratic risk , firms multisource inputs and make costly investments to make relationships with suppliers stronger (less likely to fail).
Revised:  Due to the risk of such supply relationships being idiosyncratically disrupted , firms multisource inputs and make costly investments to make relationships with suppliers stronger (less likely to fail).
Edit intent: clarity
Original:  Relationships may fail, and given this idosyncratic risk , firms multisource inputs and make costly investments to make relationships with suppliers stronger (less likely to fail).
Revised:  Relationships may fail, and given this idosyncratic risk , firms multisource inputs and invest to make relationships with suppliers stronger (less likely to fail).
Edit intent: clarity
Original:  Firms source several essential inputs through relationships with other firms.
Revised:  Each firm sources several essential inputs through relationships with other firms.
Edit intent: fluency
Original:  Due to the risk of such supply relationships being idiosyncratically disrupted, firms multisource inputs and  invest to make relationships with suppliers stronger.
Revised:  Due to the risk of such supply relationships being idiosyncratically disrupted, firms multisource inputs and strategically invest to make relationships with suppliers stronger.
Edit intent: clarity
Original:  In equilibrium, aggregate production is robust to idiosyncratic disruptions.
Revised:  Aggregate production is robust to idiosyncratic disruptions.
Edit intent: clarity
Original:  Due to the risk of such supply relationships being idiosyncratically disrupted, firms multisource inputs and strategically invest to make relationships with suppliers stronger.
Revised:  Individual supply relationships are at risk of idiosyncratic failure, which threatens to disrupt production. To protect against this, firms multisource inputs and strategically invest to make relationships with suppliers stronger.
Edit intent: clarity
Original:  However , there is a regime in which equilibrium supply networks are fragile, with small aggregate shocks to relationships causing arbitrarily steep drops in output  .
Revised:  Nevertheless , there is a regime in which equilibrium supply networks are fragile, with small aggregate shocks to relationships causing arbitrarily steep drops in output .
Edit intent: coherence
Original:  However , there is a regime in which equilibrium supply networks are fragile, with small aggregate shocks to relationships causing arbitrarily steep drops in output  .
Revised:  However , there is a regime in which arbitrarily small systemic shocks cause arbitrarily steep drops in output .
Edit intent: clarity
Original: In this paper , a method is proposed for rigorously analyzing the sign-change structure of solutions to elliptic problems with computer-assistance.
Revised: This paper proposes a method for rigorously analyzing the sign-change structure of solutions to elliptic problems with computer-assistance.
Edit intent: clarity