wanyu/IteraTeR_v2 huggingface dataset:
Original:  The former , together with the known smoothed efficient algorithm for the local-max-cut problem,  gives an alternate efficient smoothed algorithm for the 2-strategy games .
Revised:  The former together with the known smoothed efficient algorithm for the local-max-cut problem, gives an alternate efficient smoothed algorithm for the 2-strategy games .
Edit intent: fluency
Original:  The former , together with the known smoothed efficient algorithm for the local-max-cut problem,  gives an alternate efficient smoothed algorithm for the 2-strategy games .
Revised:  The former , together with the known smoothed efficient algorithm for the local-max-cut problem, gives an alternate efficient smoothed algorithm for the 2-strategy case .
Edit intent: clarity
Original:  This notion of reduction may be utilized to extend smoothed efficient algorithms from one problem to another.
Revised:  This notion of reduction allows for the extension of smoothed efficient algorithms from one problem to another.
Edit intent: clarity
Original:  For the first set of results, we develop techniques to analyze the probability of a slow increase in potential during the better-response algorithm for a perturbed game, by building on and significantly extending the recent approaches for smoothed analysis of local-max-cut [ ER'14,ABPW'17 ] . We note that network coordination games are far more general than local-max-cut since the latter reduces to a 2-strategy case of the former.
Revised:  For the first set of results, we develop techniques to bound the probability that an (adversarial) better-response algorithm for a perturbed game, by building on and significantly extending the recent approaches for smoothed analysis of local-max-cut [ ER'14,ABPW'17 ] . We note that network coordination games are far more general than local-max-cut since the latter reduces to a 2-strategy case of the former.
Edit intent: clarity
Original:  For the first set of results, we develop techniques to analyze the probability of a slow increase in potential during the better-response algorithm for a perturbed game, by building on and significantly extending the recent approaches for smoothed analysis of local-max-cut [ ER'14,ABPW'17 ] . We note that network coordination games are far more general than local-max-cut since the latter reduces to a 2-strategy case of the former.
Revised:  For the first set of results, we develop techniques to analyze the probability of a slow increase in potential during the better-response sequence makes slow improvements on the potential. Our approach combines and generalizes the local-max-cut approaches of [ ER'14,ABPW'17 ] . We note that network coordination games are far more general than local-max-cut since the latter reduces to a 2-strategy case of the former.
Edit intent: clarity
Original:  For the first set of results, we develop techniques to analyze the probability of a slow increase in potential during the better-response algorithm for a perturbed game, by building on and significantly extending the recent approaches for smoothed analysis of local-max-cut [ ER'14,ABPW'17 ] . We note that network coordination games are far more general than local-max-cut since the latter reduces to a 2-strategy case of the former.
Revised:  For the first set of results, we develop techniques to analyze the probability of a slow increase in potential during the better-response algorithm for a perturbed game, by building on and significantly extending the recent approaches for smoothed analysis of local-max-cut [ ER14,ABPW17 ] . We note that network coordination games are far more general than local-max-cut since the latter reduces to a 2-strategy case of the former.
Edit intent: fluency
Original:  Our techniques may be of independent interest to perform smoothed analysis of other potential  /  congestion games.
Revised:  Our techniques may be of independent interest to perform smoothed analysis of other potential and / congestion games.
Edit intent: fluency
Original:  Our techniques may be of independent interest to perform smoothed analysis of other potential  /  congestion games.
Revised:  Our techniques may be of independent interest to perform smoothed analysis of other potential / or congestion games.
Edit intent: fluency
Original: The two most fundamental processes describing change in biology -development and evolution- occur over drastically different timescales, difficult to reconcile within a unified framework.
Revised: The two most fundamental processes describing change in biology , development and evolu-tion, occur over drastically different timescales, difficult to reconcile within a unified framework.
Edit intent: fluency
Original:  Development involves a temporal sequence of cell states controlled by a hierarchy of regulatory structures.
Revised:  Development involves temporal sequences of cell states controlled by a hierarchy of regulatory structures.
Edit intent: fluency
Original:  Development involves a temporal sequence of cell states controlled by a hierarchy of regulatory structures.
Revised:  Development involves a temporal sequence of cell states controlled by hierarchies of regulatory structures.
Edit intent: fluency
Original:  Evolution, by contrast entails genotypic change through the acquisition or loss of genes , and involves the emergence of new, environmentally selected phenotypes over the lifetimes of many individ- uals .
Revised:  Evolution, by contrast entails genotypic change through the acquisition / loss of genes , and involves the emergence of new, environmentally selected phenotypes over the lifetimes of many individ- uals .
Edit intent: fluency
Original:  Evolution, by contrast entails genotypic change through the acquisition or loss of genes , and involves the emergence of new, environmentally selected phenotypes over the lifetimes of many individ- uals .
Revised:  Evolution, by contrast entails genotypic change through the acquisition or loss of genes , and involves the emergence of new, environmentally selected phenotypes over the lifetimes of many individuals .
Edit intent: fluency
Original:  We extend the framework of boolean models of gene regulatory network (GRN)-currently only applicable to describing development-to include evolutionary processes.
Revised:  We extend the framework of Boolean models of gene regulatory network (GRN)-currently only applicable to describing development-to include evolutionary processes.
Edit intent: fluency
Original:  We extend the framework of boolean models of gene regulatory network (GRN)-currently only applicable to describing development-to include evolutionary processes.
Revised:  We extend the framework of boolean models of gene regulatory networks (GRN)-currently only applicable to describing development-to include evolutionary processes.
Edit intent: fluency
Original:  We extend the framework of boolean models of gene regulatory network (GRN)-currently only applicable to describing development-to include evolutionary processes.
Revised:  We extend the framework of boolean models of gene regulatory network (GRN)-currently only applicable to describing development to include evolutionary processes.
Edit intent: fluency
Original:  A pheno- type may now correspond to multiple attractors, and its formal definition no longer require a fixed size for the genotype.
Revised:  A phenotype may now correspond to multiple attractors, and its formal definition no longer require a fixed size for the genotype.
Edit intent: fluency
Original:  A pheno- type may now correspond to multiple attractors, and its formal definition no longer require a fixed size for the genotype.
Revised:  A pheno- type may now correspond to multiple attractors, and its formal definition no longer requires a fixed size for the genotype.
Edit intent: fluency
Original: Anderson mixing (or Anderson acceleration) is an efficient acceleration method for fixed point iterations (i.e., x_{t+1}=G(x_t) ) , e.g., gradient descent can be viewed as iteratively applying the operation G(x) = x-\alpha\nabla f(x).
Revised: Anderson mixing (or Anderson acceleration) is an efficient acceleration method for fixed point iterations x_{t+1}=G(x_t) ) , e.g., gradient descent can be viewed as iteratively applying the operation G(x) = x-\alpha\nabla f(x).
Edit intent: coherence
Original: Anderson mixing (or Anderson acceleration) is an efficient acceleration method for fixed point iterations (i.e., x_{t+1}=G(x_t) ) , e.g., gradient descent can be viewed as iteratively applying the operation G(x) = x-\alpha\nabla f(x).
Revised: Anderson mixing (or Anderson acceleration) is an efficient acceleration method for fixed point iterations (i.e., x_{t+1}=G(x_t) , e.g., gradient descent can be viewed as iteratively applying the operation G(x) = x-\alpha\nabla f(x).
Edit intent: fluency
Original:  First , we show that Anderson mixing with Chebyshev polynomial parameters can achieve the optimal convergence rate O(\kappa\ln1{\epsilon}), which improves the previous result O(\kappa\ln1{\epsilon}) provided by [Toth and Kelley, 2015] for quadratic functions.
Revised:  In this paper , we show that Anderson mixing with Chebyshev polynomial parameters can achieve the optimal convergence rate O(\kappa\ln1{\epsilon}), which improves the previous result O(\kappa\ln1{\epsilon}) provided by [Toth and Kelley, 2015] for quadratic functions.
Edit intent: coherence
Original:  Besides, if the hyperparameters (e.g., the Lipschitz smooth parameter L) are not available, we propose a Guessing Algorithm for guessing them dynamically and also prove a similar convergence rate.
Revised:  Besides, if the hyperparameters (e.g., the Lipschitz smooth parameter L) are not available, we propose a guessing algorithm for guessing them dynamically and also prove a similar convergence rate.
Edit intent: fluency
Original: Anderson mixing (or Anderson acceleration ) is an efficient acceleration method for fixed point iterations x_{t+1}=G(x_t), e.g., gradient descent can be viewed as iteratively applying the operation G(x) = x-\alpha\nabla f(x).
Revised: Anderson acceleration (or Anderson acceleration ) is an efficient acceleration method for fixed point iterations x_{t+1}=G(x_t), e.g., gradient descent can be viewed as iteratively applying the operation G(x) = x-\alpha\nabla f(x).
Edit intent: clarity
Original: Anderson mixing (or Anderson acceleration ) is an efficient acceleration method for fixed point iterations x_{t+1}=G(x_t), e.g., gradient descent can be viewed as iteratively applying the operation G(x) = x-\alpha\nabla f(x).
Revised: Anderson mixing (or Anderson mixing ) is an efficient acceleration method for fixed point iterations x_{t+1}=G(x_t), e.g., gradient descent can be viewed as iteratively applying the operation G(x) = x-\alpha\nabla f(x).
Edit intent: clarity
Original:  In this paper, we show that Anderson mixing with Chebyshev polynomial parameters can achieve the optimal convergence rate O(\kappa\ln1{\epsilon}), which improves the previous result O(\kappa\ln1{\epsilon}) provided by Toth and Kelley, 2015  for quadratic functions.
Revised:  In this paper, we show that Anderson mixing with Chebyshev polynomial can achieve the optimal convergence rate O(\kappa\ln1{\epsilon}), which improves the previous result O(\kappa\ln1{\epsilon}) provided by Toth and Kelley, 2015 for quadratic functions.
Edit intent: clarity
Original:  In this paper, we show that Anderson mixing with Chebyshev polynomial parameters can achieve the optimal convergence rate O(\kappa\ln1{\epsilon}), which improves the previous result O(\kappa\ln1{\epsilon}) provided by Toth and Kelley, 2015  for quadratic functions.
Revised:  In this paper, we show that Anderson mixing with Chebyshev polynomial parameters can achieve the optimal convergence rate O(\kappa\ln1{\epsilon}), which improves the previous result O(\kappa\ln1{\epsilon}) provided by (Toth Kelley, 2015 for quadratic functions.
Edit intent: clarity
Original:  In this paper, we show that Anderson mixing with Chebyshev polynomial parameters can achieve the optimal convergence rate O(\kappa\ln1{\epsilon}), which improves the previous result O(\kappa\ln1{\epsilon}) provided by Toth and Kelley, 2015  for quadratic functions.
Revised:  In this paper, we show that Anderson mixing with Chebyshev polynomial parameters can achieve the optimal convergence rate O(\kappa\ln1{\epsilon}), which improves the previous result O(\kappa\ln1{\epsilon}) provided by Toth and Kelley, 2015 ) for quadratic functions.
Edit intent: fluency
Original:  Then , we provide a convergence analysis for minimizing general nonlinear problems.
Revised:  Moreover , we provide a convergence analysis for minimizing general nonlinear problems.
Edit intent: coherence
Original:  FRESH leverages on a locality sensitive hashing scheme for detecting candidate near neighbors of the query curve, and  a subsequent pruning step based on a pipeline of curve simplifications.
Revised:  FRESH leverages on a locality sensitive hashing scheme for detecting candidate near neighbors of the query curve, and on a subsequent pruning step based on a pipeline of curve simplifications.
Edit intent: fluency
Original:  FRESH leverages on a locality sensitive hashing scheme for detecting candidate near neighbors of the query curve, and  a subsequent pruning step based on a pipeline of curve simplifications.
Revised:  FRESH leverages on a locality sensitive hashing scheme for detecting candidate near neighbors of the query curve, and a subsequent pruning step based on a cascade of curve simplifications.
Edit intent: clarity
Original:  By deriving an approximate mean-field description of the global network dynamics , we show that this task admits several classes of solutions, characterized by different stability properties.
Revised:  By deriving an approximate mean-field description of the global network dynamics , we show that this task admits several classes of solutions, which imply different stability properties.
Edit intent: clarity
Original:  These classes of solutions differ in the geometrical arrangement of the readout with respect to the input vectors, defined in the high-dimensional space spanned by the network population.
Revised:  Different classes are characterized in terms of the geometrical arrangement of the readout with respect to the input vectors, defined in the high-dimensional space spanned by the network population.
Edit intent: clarity
Original:  We show that our theoretical approach can be used to understand how standard training techniques implement the input-output task in finite-size feedback networks.
Revised:  We find that such approximate theoretical approach can be used to understand how standard training techniques implement the input-output task in finite-size feedback networks.
Edit intent: clarity
Original:  In particular, our approximate description captures the local and the global stability properties of the target solution, and  predicts training performance.
Revised:  In particular, our simplified description captures the local and the global stability properties of the target solution, and predicts training performance.
Edit intent: clarity
Original:  In particular, our approximate description captures the local and the global stability properties of the target solution, and  predicts training performance.
Revised:  In particular, our approximate description captures the local and the global stability properties of the target solution, and thus predicts training performance.
Edit intent: coherence
Original:  While a lot of effort has been put on the problem of finding a single dense subgraph, only recently the focus has been shifted to the problem of finding a set of dens- est subgraphs.
Revised:  While a lot of effort has been put on the problem of finding a single dense subgraph, only recently the focus has been shifted to the problem of finding a set of densest subgraphs.
Edit intent: fluency
Original:  This has triggered the interest in developing mmWave vehicular communication solutions that can solve the challenges resulting from the use of high-frequency bands and the high mobility of nodes .
Revised:  This has triggered the interest in developing mmWave vehicular communications. However, solutions are necessary to solve the challenges resulting from the use of high-frequency bands and the high mobility of nodes .
Edit intent: coherence
Original:  This has triggered the interest in developing mmWave vehicular communication solutions that can solve the challenges resulting from the use of high-frequency bands and the high mobility of nodes .
Revised:  This has triggered the interest in developing mmWave vehicular communication solutions that can solve the challenges resulting from the use of high-frequency bands and the high mobility of vehicles .
Edit intent: clarity
Original:  This approach improves the operation of the MAC as the control functions benefit from the longer range and omnidirectional transmissions of sub-6GHz V2X technologies.
Revised:  This approach improves the operation of the MAC as the control functions benefit from the longer range , and the broadcast and omnidirectional transmissions of sub-6GHz V2X technologies.
Edit intent: clarity
Original:  The conducted study demonstrates that the proposed sub-6GHz assisted mmWave MAC reduces the control overhead and delay, and increases the spatial sharing compared to a standard IEEE 802.
Revised:  This simulation study demonstrates that the proposed sub-6GHz assisted mmWave MAC reduces the control overhead and delay, and increases the spatial sharing compared to a standard IEEE 802.
Edit intent: clarity
Original: 11ad  . The proposed MAC is evaluated in this study for V2V communications with 802.11p in the control plane and 802.11ad in the data plane.
Revised: 11ad . The proposed MAC is here evaluated for V2V communications with 802.11p in the control plane and 802.11ad in the data plane.
Edit intent: clarity
Original: 11ad  . The proposed MAC is evaluated in this study for V2V communications with 802.11p in the control plane and 802.11ad in the data plane.
Revised: 11ad . The proposed MAC is evaluated in this study for V2V communications using 802.11p in the control plane and 802.11ad in the data plane.
Edit intent: fluency
Original: 11ad  . The proposed MAC is evaluated in this study for V2V communications with 802.11p in the control plane and 802.11ad in the data plane.
Revised: 11ad . The proposed MAC is evaluated in this study for V2V communications with 802.11p for the control plane and 802.11ad in the data plane.
Edit intent: clarity
Original: 11ad  . The proposed MAC is evaluated in this study for V2V communications with 802.11p in the control plane and 802.11ad in the data plane.
Revised: 11ad . The proposed MAC is evaluated in this study for V2V communications with 802.11p in the control plane and 802.11ad for the data plane.
Edit intent: clarity
Original:  However, the proposal is not restricted to these technologies, and can be adapted to other technologies such as LTE-V or Cellular V2X and 5G NR.
Revised:  However, the proposal is not restricted to these technologies, and can be adapted to other technologies such as C-V2X and 5G NR.
Edit intent: coherence
Original:  A series of recent breakthroughs has resulted in an ultra-efficient streaming algorithm for this problem that requires only O(k \log m{k}) space [Clifford, Kociumaka, Porat, 2017 ].
Revised:  A series of recent breakthroughs have resulted in an ultra-efficient streaming algorithm for this problem that requires only O(k \log m{k}) space [Clifford, Kociumaka, Porat, 2017 ].
Edit intent: fluency
Original:  In this work  we consider a strictly harder problem called dictionary matching with k mismatches, where we are given a dictionary of d patterns of lengths \le m and must find all their k-mismatch occurrences in the text, and show the first streaming algorithm for it.
Revised:  In this work , we consider a strictly harder problem called dictionary matching with k mismatches, where we are given a dictionary of d patterns of lengths \le m and must find all their k-mismatch occurrences in the text, and show the first streaming algorithm for it.
Edit intent: fluency
Original:  A series of recent breakthroughs have resulted in an ultra-efficient streaming algorithm for this problem that requires only O(k \log \frac{m{k}) space and O(\log n{k} (k \log k + \log^3 n)) time per letter } [Clifford, Kociumaka, Porat, SODA 2019].
Revised:  A series of recent breakthroughs have resulted in an ultra-efficient streaming algorithm for this problem that requires only O(k \log \frac{n{k}) space and O(\log n{k} (k \log k + \log^3 n)) time per letter } [Clifford, Kociumaka, Porat, SODA 2019].
Edit intent: clarity
Original:  In this work, we consider a strictly harder problem called dictionary matching with k mismatches , where we are given a dictionary of d patterns of lengths%DIFDELCMD < \le %%% m and must find all their k-mismatch occurrences in the text , and show the first streaming algorithm for it.
Revised:  In this work, we consider a strictly harder problem called dictionary matching with k mismatches . In this problem, we are given a dictionary of d patterns of lengths%DIFDELCMD < \le %%% m and must find all their k-mismatch occurrences in the text , and show the first streaming algorithm for it.
Edit intent: coherence
Original:  In this work, we consider a strictly harder problem called dictionary matching with k mismatches , where we are given a dictionary of d patterns of lengths%DIFDELCMD < \le %%% m and must find all their k-mismatch occurrences in the text , and show the first streaming algorithm for it.
Revised:  In this work, we consider a strictly harder problem called dictionary matching with k mismatches , where we are given a dictionary of d patterns %DIFDELCMD < \le %%% m and must find all their k-mismatch occurrences in the text , and show the first streaming algorithm for it.
Edit intent: fluency
Original:  The algorithm uses O(k d \log^k d \, polylog\, m)space and processes each position of the text in O(k \log^{k} d \, \mathrm{polylog\, m }  + occ) time , where occ is the number of k-mismatch occurrences of the patterns that end at this position .
Revised:  The algorithm uses O(k d \log^k d \, polylog\, m)space and processes each position of the text in O(k \log^{k} d \, m } + occ) time , where occ is the number of k-mismatch occurrences of the patterns that end at this position .
Edit intent: clarity
Original:  The dNEF measure is shown to be more repro- ducible and robust than P values and requires sample sizes as small as 3 to reproducibly identify differentially abundant features.
Revised:  The dNEF measure is shown to be more reproducible and robust than P values and requires sample sizes as small as 3 to reproducibly identify differentially abundant features.
Edit intent: fluency
Original:  Availability: Source code and binaries freely available at: URL  omicplotR, and URL 
Revised:  Availability: Source code and binaries freely available at: URL , omicplotR, and URL 
Edit intent: fluency
Original:  Availability: Source code and binaries freely available at: URL  omicplotR, and URL 
Revised:  Availability: Source code and binaries freely available at: URL omicplotR, and URL .
Edit intent: fluency
Original: Recent advances in Deep Reinforcement Learning and Robotics have been driven by the presence of increasingly realistic and complex simulation environments.
Revised: Recent advances in artificial intelligence have been driven by the presence of increasingly realistic and complex simulation environments.
Edit intent: clarity
Original:  Many of the existing platforms, however, provide either unrealistic visuals, inaccurate physics, low task complexity,  or a limited capacity for interaction among artificial agents.
Revised:  Many of the existing environments provide either unrealistic visuals, inaccurate physics, low task complexity, or a limited capacity for interaction among artificial agents.
Edit intent: clarity