wanyu/IteraTeR_v2 huggingface dataset:
Original:  Less explored is the potential of machine learning in the discovery of physical laws from observational datathrough interpretable models.
Revised:  Less explored is its use to discover interpretable physical laws from observational datathrough interpretable models.
Edit intent: clarity
Original:  The resulting parsimonious neural networks are easily interpretable as Newton's second law  expressed as a non-trivial time integrator that exhibits time-reversibility and conserves energy .
Revised:  The resulting parsimonious neural networks are easily interpretable as Newton's second law , expressed as a non-trivial time integrator that exhibits time-reversibility and conserves energy .
Edit intent: fluency
Original: Multiple random walks is a model for movement of several independent random walkers on a graph, and it is applied to various graph algorithms.
Revised: Multiple random walks are the movement of several independent random walkers on a graph, and it is applied to various graph algorithms.
Edit intent: clarity
Original: Multiple random walks is a model for movement of several independent random walkers on a graph, and it is applied to various graph algorithms.
Revised: Multiple random walks is a model for movement of several independent random walkers on a graph, and are applied to various graph algorithms.
Edit intent: fluency
Original:  In order to design an efficient graph algorithm using multiple random walks, it is essential to study theoretical considerations for deeply understanding the characteristicsof graph algorithms .
Revised:  In order to design an efficient graph algorithm based on multiple random walks, it is essential to study theoretical considerations for deeply understanding the characteristicsof graph algorithms .
Edit intent: fluency
Original:  In order to design an efficient graph algorithm using multiple random walks, it is essential to study theoretical considerations for deeply understanding the characteristicsof graph algorithms .
Revised:  In order to design an efficient graph algorithm using multiple random walks, it is essential to study multiple random walks theoretically for deeply understanding the characteristicsof graph algorithms .
Edit intent: clarity
Original:  In order to design an efficient graph algorithm using multiple random walks, it is essential to study theoretical considerations for deeply understanding the characteristicsof graph algorithms .
Revised:  In order to design an efficient graph algorithm using multiple random walks, it is essential to study theoretical considerations for deeply understanding their characteristics .
Edit intent: clarity
Original:  The first meeting time is defined as the time it takes for multiple random walkers to meet on a same node .
Revised:  The first meeting time on a graph is defined by the time it takes for multiple random walkers to meet on a same node .
Edit intent: clarity
Original:  In various works, the first meeting time of multiple random walk has been analyzed.
Revised:  In various works, the first meeting time of multiple random walks has been analyzed.
Edit intent: fluency
Original:  However, many of these previous works focused on regular graphs.
Revised:  However, many of these previous works focus on regular graphs.
Edit intent: fluency
Original:  In this paper, we analyze  first meeting time of multiple random walks in arbitrary graph , and clarify the effect of graph structures on its expected value.
Revised:  In this paper, we analyze the first meeting time of multiple random walks in arbitrary graph , and clarify the effect of graph structures on its expected value.
Edit intent: fluency
Original:  In this paper, we analyze  first meeting time of multiple random walks in arbitrary graph , and clarify the effect of graph structures on its expected value.
Revised:  In this paper, we analyze first meeting time of multiple random walks in arbitrary graphs , and clarify the effect of graph structures on its expected value.
Edit intent: fluency
Original:  First, we derive the spectral formula for the expected first meeting time of two random walkers using the spectral graph theory.
Revised:  First, we derive the spectral formula of the expected first meeting time of two random walkers using the spectral graph theory.
Edit intent: fluency
Original:  First, we derive the spectral formula for the expected first meeting time of two random walkers using the spectral graph theory.
Revised:  First, we derive the spectral formula for the expected first meeting time on the basis of the spectral graph theory.
Edit intent: clarity
Original:  Then,  the principal component of the expected first meeting time are examined using the derived spectral formula.
Revised:  Then, we examine the principal component of the expected first meeting time are examined using the derived spectral formula.
Edit intent: clarity
Original:  Then,  the principal component of the expected first meeting time are examined using the derived spectral formula.
Revised:  Then, the principal component of the expected first meeting time using the derived spectral formula.
Edit intent: clarity
Original:  The resulting principal component reveals that (a)the expected first meeting time is almost dominated by n/(1+d_{\rm std}^2/d_{\rm avg}^2)
Revised:  The clarified principal component reveals that (a)the expected first meeting time is almost dominated by n/(1+d_{\rm std}^2/d_{\rm avg}^2)
Edit intent: clarity
Original: Multiple random walksare the movement of several independent random walkers on a graph , and are applied to various graph algorithms.
Revised: Various graph algorithms have been developed with multiple random walks, the movement of several independent random walkers on a graph , and are applied to various graph algorithms.
Edit intent: clarity
Original:  In order to design an efficient graph algorithm based on multiple random walks , it is essential to study multiple random walks theoretically for deeply understanding their characteristics.
Revised:  In order to design an efficient graph algorithm based on multiple random walks requires investigating multiple random walks theoretically for deeply understanding their characteristics.
Edit intent: clarity
Original:  In order to design an efficient graph algorithm based on multiple random walks , it is essential to study multiple random walks theoretically for deeply understanding their characteristics.
Revised:  In order to design an efficient graph algorithm based on multiple random walks , it is essential to study multiple random walks theoretically to attain a deep understanding of their characteristics.
Edit intent: clarity
Original:  The first meeting time is one of the important metrics for the multiple random walks.
Revised:  The first meeting time is one of the important metrics for multiple random walks.
Edit intent: fluency
Original:  The first meeting time is closely related to the rendezvous problem, which is are a fundamental problem in the field of computer science.
Revised:  The first meeting time is closely related to the rendezvous problem, a fundamental problem in the field of computer science.
Edit intent: clarity
Original:  The first meeting time is closely related to the rendezvous problem, which is are a fundamental problem in the field of computer science.
Revised:  The first meeting time is closely related to the rendezvous problem, which is are a fundamental problem in computer science.
Edit intent: clarity
Original:  In previous works, the first meeting time of multiple random walks has been analyzed .
Revised:  The first meeting time of multiple random walks has been analyzed .
Edit intent: clarity
Original:  However, many of these previous works focus on regular graphs.
Revised:  However, many of these analyses have focused on regular graphs.
Edit intent: clarity
Original:  In this paper, we analyze the first meeting time of multiple random walks in arbitrary graphs , and clarify the effect of graph structures on its expected value .
Revised:  In this paper, we analyze the first meeting time of multiple random walks in arbitrary graphs and clarify the effect of graph structures on its expected value .
Edit intent: fluency
Original:  In this paper, we analyze the first meeting time of multiple random walks in arbitrary graphs , and clarify the effect of graph structures on its expected value .
Revised:  In this paper, we analyze the first meeting time of multiple random walks in arbitrary graphs , and clarify the effects of graph structures on its expected value .
Edit intent: fluency
Original:  In this paper, we analyze the first meeting time of multiple random walks in arbitrary graphs , and clarify the effect of graph structures on its expected value .
Revised:  In this paper, we analyze the first meeting time of multiple random walks in arbitrary graphs , and clarify the effect of graph structures on expected values .
Edit intent: clarity
Original:  First, we derive the spectral formula of the expected first meeting time on the basis of the spectral graph theory.
Revised:  First, we derive the spectral formula of the expected first meeting time on the basis of spectral graph theory.
Edit intent: fluency
Original:  The characteristics (a) is useful to understand the effect of the graph structure on the first meeting time.
Revised:  The characteristic (a) is useful to understand the effect of the graph structure on the first meeting time.
Edit intent: fluency
Original:  The characteristics (a) is useful to understand the effect of the graph structure on the first meeting time.
Revised:  The characteristics (a) is useful for understanding the effect of the graph structure on the first meeting time.
Edit intent: fluency
Original:  We apply the method of polynomial interpolation, for which we prove that \sum_x e^{ f (x)} \ne 0 for complex a _{ij and b_i such that \sum_j |\Re}%DIFDELCMD < \thinspace %%% a _{ij| \leq 1-\delta, \sum_j |\Im}%DIFDELCMD < \thinspace %%% a_{ij| \leq \delta^2/10 and |\Im}%DIFDELCMD < \thinspace %%% b_i| \leq \delta^2/10 for all i, which is  interpreted as the absence of a phase transition in the Lee - Yang sense in the corresponding Ising model.
Revised:  We apply the method of polynomial interpolation, for which we prove that \sum_x e^{ (x)} \ne 0 for complex a _{ij and b_i such that \sum_j |\Re}%DIFDELCMD < \thinspace %%% a _{ij| \leq 1-\delta, \sum_j |\Im}%DIFDELCMD < \thinspace %%% a_{ij| \leq \delta^2/10 and |\Im}%DIFDELCMD < \thinspace %%% b_i| \leq \delta^2/10 for all i, which is interpreted as the absence of a phase transition in the Lee - Yang sense in the corresponding Ising model.
Edit intent: clarity
Original:  We apply the method of polynomial interpolation, for which we prove that \sum_x e^{ f (x)} \ne 0 for complex a _{ij and b_i such that \sum_j |\Re}%DIFDELCMD < \thinspace %%% a _{ij| \leq 1-\delta, \sum_j |\Im}%DIFDELCMD < \thinspace %%% a_{ij| \leq \delta^2/10 and |\Im}%DIFDELCMD < \thinspace %%% b_i| \leq \delta^2/10 for all i, which is  interpreted as the absence of a phase transition in the Lee - Yang sense in the corresponding Ising model.
Revised:  We apply the method of polynomial interpolation, for which we prove that \sum_x e^{ f (x)} \ne 0 for complex a _{ij and b_i such that \sum_j |\Re}%DIFDELCMD < \thinspace %%% | \leq 1-\delta, \sum_j |\Im}%DIFDELCMD < \thinspace %%% a_{ij| \leq \delta^2/10 and |\Im}%DIFDELCMD < \thinspace %%% b_i| \leq \delta^2/10 for all i, which is interpreted as the absence of a phase transition in the Lee - Yang sense in the corresponding Ising model.
Edit intent: fluency
Original:  We apply the method of polynomial interpolation, for which we prove that \sum_x e^{ f (x)} \ne 0 for complex a _{ij and b_i such that \sum_j |\Re}%DIFDELCMD < \thinspace %%% a _{ij| \leq 1-\delta, \sum_j |\Im}%DIFDELCMD < \thinspace %%% a_{ij| \leq \delta^2/10 and |\Im}%DIFDELCMD < \thinspace %%% b_i| \leq \delta^2/10 for all i, which is  interpreted as the absence of a phase transition in the Lee - Yang sense in the corresponding Ising model.
Revised:  We apply the method of polynomial interpolation, for which we prove that \sum_x e^{ f (x)} \ne 0 for complex a _{ij and b_i such that \sum_j |\Re}%DIFDELCMD < \thinspace %%% a _{ij| \leq 1-\delta, \sum_j |\Im}%DIFDELCMD < \thinspace %%% | \leq \delta^2/10 and |\Im}%DIFDELCMD < \thinspace %%% b_i| \leq \delta^2/10 for all i, which is interpreted as the absence of a phase transition in the Lee - Yang sense in the corresponding Ising model.
Edit intent: fluency
Original: De novo therapeutic design is challenged by a vast chemical repertoire and multiple constraints such as high broad-spectrum potency and low toxicity.
Revised: De novo therapeutic design is challenged by a vast chemical repertoire and multiple constraints , e.g., high broad-spectrum potency and low toxicity.
Edit intent: coherence
Original:  We further screen the generated molecules by using a set of deep learning classifiers in conjunction with novel physicochemical features derived from high-throughput molecular simulations.
Revised:  We screen the generated molecules by using a set of deep learning classifiers in conjunction with novel physicochemical features derived from high-throughput molecular simulations.
Edit intent: clarity
Original:  We further screen the generated molecules by using a set of deep learning classifiers in conjunction with novel physicochemical features derived from high-throughput molecular simulations.
Revised:  We further screen the generated molecules by using a set of deep learning classifiers in conjunction with novel features derived from high-throughput molecular simulations.
Edit intent: clarity
Original:  We further screen the generated molecules by using a set of deep learning classifiers in conjunction with novel physicochemical features derived from high-throughput molecular simulations.
Revised:  We further screen the generated molecules by using a set of deep learning classifiers in conjunction with novel physicochemical features derived from atomistic simulations.
Edit intent: clarity
Original:  The proposed approach is employed for designing non-toxic antimicrobial peptides (AMPs) with strong broad-spectrum potency, which are emerging drug candidates for tackling antibiotic resistance.
Revised:  The proposed approach is demonstrated for designing non-toxic antimicrobial peptides (AMPs) with strong broad-spectrum potency, which are emerging drug candidates for tackling antibiotic resistance.
Edit intent: clarity
Original:  The proposed approach thus presents a viable path for faster  discovery of potent and selective broad-spectrum antimicrobials with a higher success rate than state-of-the-art methods .
Revised:  The proposed approach thus presents a viable path for faster discovery of potent and selective broad-spectrum antimicrobials .
Edit intent: clarity
Original:  However, ESOP can flexibly interact with arbitrary epidemiological simulators  and produce schedules that involve multiple phases of lock-downs.
Revised:  However, ESOP is flexible enough to interact with arbitrary epidemiological simulators and produce schedules that involve multiple phases of lock-downs.
Edit intent: clarity
Original:  In the case of Persistent Object Stores, previous approaches to prefetching have been based on predictions made through analysis of the store's schema, which generates rigid predictions, or monitoring the access patterns to the store while applications are executed, which introduces memory and/or computation overhead.
Revised:  In the case of Persistent Object Stores, previous approaches to prefetching have been based on predictions made through analysis of the store's schema, which generates rigid predictions, or monitoring access patterns to the store while applications are executed, which introduces memory and/or computation overhead.
Edit intent: fluency
Original:  In this paper, we present CAPre, a novel prefetching system for Persistent Object Stores based on static code analysis for object-oriented applications.
Revised:  In this paper, we present CAPre, a novel prefetching system for Persistent Object Stores based on static code analysis of object-oriented applications.
Edit intent: fluency
Original:  Moreover, given that CAPre is able to predict large amounts of objects that will be accessed in the near future, it enables the object store to perform parallel prefetching if the objects are distributed, in a much more aggressive way than in schema-based prediction algorithms.
Revised:  Moreover, CAPre is able to predict large amounts of objects that will be accessed in the near future, it enables the object store to perform parallel prefetching if the objects are distributed, in a much more aggressive way than in schema-based prediction algorithms.
Edit intent: coherence
Original:  Moreover, given that CAPre is able to predict large amounts of objects that will be accessed in the near future, it enables the object store to perform parallel prefetching if the objects are distributed, in a much more aggressive way than in schema-based prediction algorithms.
Revised:  Moreover, given that CAPre is able to predict large amounts of objects that will be accessed in the near future, thus enabling the object store to perform parallel prefetching if the objects are distributed, in a much more aggressive way than in schema-based prediction algorithms.
Edit intent: coherence
Original:  Finally, we point out some possible policy implications of this directed structure, both for contact tracing strategy and for interventions designed to prevent super spreading events.
Revised:  Finally, we point out some possible policy implications of this directed structure, both for contact tracing strategy and for interventions designed to prevent superspreading events.
Edit intent: fluency
Original: Hierarchical modeling and learning has proven very powerful in the field of Gaussian process regression and kernel methods, especially for machine learning applications and , increasingly, within the field of inverse problemsmore generally.
Revised: Gaussian process regression has proven very powerful in the field of Gaussian process regression and kernel methods, especially for machine learning applications and , increasingly, within the field of inverse problemsmore generally.
Edit intent: coherence
Original:  Here, we demonstrate an optical machine vision system that uses trainable matter in the form of diffractive layers to transform and encode the spatial information of objects into the power spectrum of the diffracted light, which is used to perform optical classification of objects with a single-pixel spectroscopic detector.
Revised:  Here, we demonstrate the design of optical networks in the form of diffractive layers to transform and encode the spatial information of objects into the power spectrum of the diffracted light, which is used to perform optical classification of objects with a single-pixel spectroscopic detector.
Edit intent: clarity
Original:  Here, we demonstrate an optical machine vision system that uses trainable matter in the form of diffractive layers to transform and encode the spatial information of objects into the power spectrum of the diffracted light, which is used to perform optical classification of objects with a single-pixel spectroscopic detector.
Revised:  Here, we demonstrate an optical machine vision system that uses trainable matter in the form of diffractive layers to transform and encode the spatial information of objects into the power spectrum of the diffracted light, which are used to perform optical classification of objects with a single-pixel spectroscopic detector.
Edit intent: fluency
Original:  This unique  framework merges the power of deep learning with the spatial and spectral processing capabilities of trainable matter , and can also be extended to other spectral-domain measurement systems to enable new 3D imaging and sensing modalities integrated with spectrally encoded classification tasks performed through diffractive  networks.
Revised:  This unique machine vision framework merges the power of deep learning with the spatial and spectral processing capabilities of trainable matter , and can also be extended to other spectral-domain measurement systems to enable new 3D imaging and sensing modalities integrated with spectrally encoded classification tasks performed through diffractive networks.
Edit intent: clarity
Original:  This unique  framework merges the power of deep learning with the spatial and spectral processing capabilities of trainable matter , and can also be extended to other spectral-domain measurement systems to enable new 3D imaging and sensing modalities integrated with spectrally encoded classification tasks performed through diffractive  networks.
Revised:  This unique framework merges the power of deep learning with the spatial and spectral processing capabilities of diffractive networks , and can also be extended to other spectral-domain measurement systems to enable new 3D imaging and sensing modalities integrated with spectrally encoded classification tasks performed through diffractive networks.
Edit intent: clarity
Original:  This unique  framework merges the power of deep learning with the spatial and spectral processing capabilities of trainable matter , and can also be extended to other spectral-domain measurement systems to enable new 3D imaging and sensing modalities integrated with spectrally encoded classification tasks performed through diffractive  networks.
Revised:  This unique framework merges the power of deep learning with the spatial and spectral processing capabilities of trainable matter , and can also be extended to other spectral-domain measurement systems to enable new 3D imaging and sensing modalities integrated with spectrally encoded classification tasks performed through diffractive optical networks.
Edit intent: clarity
Original: Modeling accurately the evolution and intervention strategies for the Covid-19 pandemic , that has now affected almost every country in the world, is a challenging problem.
Revised: Modeling accurately the evolution and intervention strategies for the Covid-19 pandemic is a challenging problem.
Edit intent: coherence
Original:  We find that for the same target value, R_0^{\rm target} <1, TQ is more efficient in controlling the pandemic than lockdowns that only implement SD.
Revised:  We find that for the same target R_0^{\rm target} <1, TQ is more efficient in controlling the pandemic than lockdowns that only implement SD.
Edit intent: clarity
Original:  We find that for the same target R_0^{\rm target < 1, TQ is more efficient in controlling the pandemic than lockdowns that only implement SD.
Revised:  We find that for the same target R_0^{\rm target < 1, TQ is more efficient in controlling the pandemic than SD.
Edit intent: clarity
Original:  Subordinates in a cluster interact with each other through reinforcement learning, and report learning information to their corresponding supervisor.
Revised:  Subordinates interact with rivals through reinforcement learning, and report learning information to their corresponding supervisor.
Edit intent: clarity
Original:  Subordinates, in turn, update learning information according to guidance, following the  win stay, lose shift  strategy.
Revised:  Subordinates, in turn, update learning information according to guidance, following the " win stay, lose shift strategy.
Edit intent: fluency
Original:  Subordinates, in turn, update learning information according to guidance, following the  win stay, lose shift  strategy.
Revised:  Subordinates, in turn, update learning information according to guidance, following the win stay, lose shift " strategy.
Edit intent: fluency
Original:  In devising a lower bound technique specific to MaxRes (and not merely inheriting lower bounds from Res), we define a new semialgebraic proof system called the SubCubeSums proof system.
Revised:  In devising a lower bound technique specific to MaxRes (and not merely inheriting lower bounds from Res), we define a new proof system called the SubCubeSums proof system.
Edit intent: clarity
Original:  This system, which p-simulates MaxResW, is a special case of the  Sherali-Adams proof system.
Revised:  This system, which p-simulates MaxResW, can be viewed as a special case of the Sherali-Adams proof system.
Edit intent: clarity