wanyu/IteraTeR_v2 huggingface dataset:
Original:  By specifying a general class of functions for price-rarity relationships, we provide the first theoretical analysis of AAE models, and show that the classic theory can understate the risk of species extinction.
Revised:  By specifying a general class of functions for price-rarity relationships, we show that the classic theory can understate the risk of species extinction.
Edit intent: clarity
Original:  The problem of extending these partial Boolean maps to non-admissible states, i.e. states that do not have a multivalued counterpart , is also investigated .
Revised:  The problem of extending these maps to non-admissible states, i.e. states that do not have a multivalued counterpart , is also investigated .
Edit intent: clarity
Original:  The problem of extending these partial Boolean maps to non-admissible states, i.e. states that do not have a multivalued counterpart , is also investigated .
Revised:  The problem of extending these partial Boolean maps to non-admissible states, i.e. states that do not have a multivalued counterpart .
Edit intent: clarity
Original:  Different extensions of the Boolean counterpart affect the structure of the regulatory graph in different ways.
Revised:  Different extensions of the Boolean conversion affect the structure of the regulatory graph in different ways.
Edit intent: clarity
Original:  Different extensions of the Boolean counterpart affect the structure of the regulatory graph in different ways.
Revised:  Different extensions of the Boolean counterpart affect the structure of the interaction graphs in different ways.
Edit intent: clarity
Original:  A particular technique for extending the Boolean unitary version of the network is identified, that ensures that no new circuits are added .
Revised:  A particular technique for extending the Boolean unitary version of the network is identified, that ensures that feedback cycles are preserved .
Edit intent: clarity
Original:  This property, combined with the preservation of the asymptotic behaviour, can prove useful for the application of results and analyses defined in the Boolean setting to multivalued networks, and vice versa.
Revised:  This property, combined with the conservation of the asymptotic behaviour, can prove useful for the application of results and analyses defined in the Boolean setting to multivalued networks, and vice versa.
Edit intent: fluency
Original:  By considering the conversion of a known example for the discrete multivalued case, we create a Boolean map showing that , for n \geq 6, the absence of fixed points is compatible with the absence of local negative circuits in the regulatory graph .
Revised:  By considering the conversion of a known example for the discrete multivalued case, we create a Boolean map showing that , for n \geq 6, the absence of fixed points are compatible with the absence of local negative circuits in the regulatory graph .
Edit intent: fluency
Original:  Interleaving strategies are also known as process-scheduling policies .
Revised:  An interleaving strategy is what is called a process-scheduling policies .
Edit intent: clarity
Original:  In this article , we discuss the role of network analysis in industrial and applied mathematics, and we give several examples of network science in industry  .
Revised:  In this commentary , we discuss the role of network analysis in industrial and applied mathematics, and we give several examples of network science in industry .
Edit intent: clarity
Original:  Because the study of networks is concerned explicitly with connectivity between different entities,  it has become very prominent in industrial settings, and this importance has been accentuated further amidst the modern data deluge.
Revised:  The study of networks is concerned explicitly with connectivity between different entities, it has become very prominent in industrial settings, and this importance has been accentuated further amidst the modern data deluge.
Edit intent: coherence
Original:  Because the study of networks is concerned explicitly with connectivity between different entities,  it has become very prominent in industrial settings, and this importance has been accentuated further amidst the modern data deluge.
Revised:  Because the study of networks is concerned explicitly with connectivity between different entities, and it has become very prominent in industrial settings, and this importance has been accentuated further amidst the modern data deluge.
Edit intent: fluency
Original:  Because the study of networks is concerned explicitly with connectivity between different entities,  it has become very prominent in industrial settings, and this importance has been accentuated further amidst the modern data deluge.
Revised:  Because the study of networks is concerned explicitly with connectivity between different entities, it has become very prominent in industrial settings, an importance that has intensified amidst the modern data deluge.
Edit intent: clarity
Original: Expressive efficiency is a concept that allows formally reasoning about the representational capacity of deep network architectures.
Revised: The driving force behind deep networks is their ability to compactly represent rich classes of functions. The primary notion for formally reasoning about the representational capacity of deep network architectures.
Edit intent: clarity
Original:  A well-known example is the exponential expressive efficiency of depth, namely, that in many cases shallow networks must grow exponentially large in order to represent functions realized by deep networks .
Revised:  A well-known example is the exponential expressive efficiency of depth, showing that deep networks are representationally superior to shallow ones .
Edit intent: clarity
Original:  In this paper we study the expressive efficiency brought forth by the architectural feature of connectivity, motivated by the observation that nearly all state of the art networks these days employ elaborate connection schemes, running layers in parallel while splitting and merging them in various ways.
Revised:  In this paper we study the expressive efficiency brought forth by connectivity, motivated by the observation that nearly all state of the art networks these days employ elaborate connection schemes, running layers in parallel while splitting and merging them in various ways.
Edit intent: coherence
Original:  We focus on dilated convolutional networks, a family of deep models gaining increased attention, underlying state of the art architectures like Google's WaveNet and ByteNet .
Revised:  We focus on dilated convolutional networks, a family of deep models delivering state of the art architectures like Google's WaveNet and ByteNet .
Edit intent: clarity
Original:  We focus on dilated convolutional networks, a family of deep models gaining increased attention, underlying state of the art architectures like Google's WaveNet and ByteNet .
Revised:  We focus on dilated convolutional networks, a family of deep models gaining increased attention, underlying state of the art performance in sequence processing tasks .
Edit intent: clarity
Original:  By introducing and studying the concept of mixed tensor decompositions, we prove that interconnecting dilated convolutional networks can lead to expressive efficiency.
Revised:  By introducing and analyzing the concept of mixed tensor decompositions, we prove that interconnecting dilated convolutional networks can lead to expressive efficiency.
Edit intent: clarity
Original:  In particular, we show that  a single connection between intermediate layers can already lead to an almost quadratic gap, which in large-scale settings typically makes the difference between a model that is practical and one that is not  .
Revised:  In particular, we show that even a single connection between intermediate layers can already lead to an almost quadratic gap, which in large-scale settings typically makes the difference between a model that is practical and one that is not .
Edit intent: coherence
Original:  We conduct hyper-parameter optimization for several classification methods using a large set of problems to benchmark the ability of FEW to improve data representations.
Revised:  We conduct a benchmark comparison to several classification methods using a large set of problems to benchmark the ability of FEW to improve data representations.
Edit intent: clarity
Original:  The results show that FEW can improve the best classifier performance on several problems .
Revised:  The results show that FEW can improve the best classifier performance in several cases .
Edit intent: clarity
Original: In this paper we extend the work of Tancer , and of Malgouyres and Franc\'es, showing that (d,k)-collapsibility is NP-complete for d\geq k+2 except (2,0).
Revised: In this paper we extend the works of Tancer and of Malgouyres and Franc\'es, showing that (d,k)-collapsibility is NP-complete for d\geq k+2 except (2,0).
Edit intent: fluency
Original: We introduce  affine OBDD model and we show that exact affine OBDDs can be exponentially narrower than bounded-error quantum and classical OBDDs on some certain problems.
Revised: We introduce the affine OBDD model and we show that exact affine OBDDs can be exponentially narrower than bounded-error quantum and classical OBDDs on some certain problems.
Edit intent: fluency
Original:  Videos available at URL 
Revised:  Videos available at URL .
Edit intent: fluency
Original: The recent growth in interest in the physics and mathematics of networks has been driven in large part by the increasing availability of data describing the structure of networks ranging from the internet and the web to social and biological networks .
Revised: Driven by growing interest in the physics and mathematics of networks has been driven in large part by the increasing availability of data describing the structure of networks ranging from the internet and the web to social and biological networks .
Edit intent: clarity
Original:  It is a surprising feature of many empirical studies, however, that the data are reported without any estimate of their expected accuracy, even though it is clear that most do suffer from measurement errorof various kinds.
Edit intent: coherence
Original:  When the underlay implements a dynamic policy, we show that the same decentralized policy performs as well as any decentralized policy.
Edit intent: coherence
Original:  More specifically, we first propose an adaptive formula for the Levenberg-Marquardt parameter and analyse the local convergence of the method under H\"{o}lder metric subregularity .
Revised:  More specifically, we propose an adaptive formula for the Levenberg-Marquardt parameter and analyse the local convergence of the method under H\"{o}lder metric subregularity .
Edit intent: coherence
Original:  We then introduce a bounded version of the Levenberg-Marquardt parameter and analyse the local convergence of the modified method under the \L ojasiewicz gradient inequality  .
Revised:  We then introduce a bounded version of the Levenberg-Marquardt parameter and analyse the local convergence of the method under the \L ojasiewicz gradient inequality .
Edit intent: clarity
Original:  We then introduce a bounded version of the Levenberg-Marquardt parameter and analyse the local convergence of the modified method under the \L ojasiewicz gradient inequality  .
Revised:  We then introduce a bounded version of the Levenberg-Marquardt parameter and analyse the local convergence of the modified method under the \L ojasiewicz gradient inequality holds .
Edit intent: clarity
Original:  More specifically, we propose an adaptive formula for the Levenberg-Marquardt parameter and analyse the local convergence of the method under H\"{o}lder metric subregularity of the function defining the equation and H\"older continuity of its gradient  .
Revised:  More specifically, we propose an adaptive formula for the Levenberg-Marquardt parameter and analyse the local convergence of the method under H\"{o}lder metric subregularity of the function defining the equation and H\"older continuity of its gradient mapping .
Edit intent: clarity
Original:  We experimentally show that it can outperform  first-order and fully recursive higher-order IVM as well as recomputation by orders of magnitude while using less memory.
Revised:  We experimentally show that it can outperform first-order and fully recursive higher-order IVM , and plain recomputation by orders of magnitude while using less memory.
Edit intent: clarity
Original:  Training of the social discrete choice models is performed using  a specialized Monte Carlo expectation maximization  algorithm.
Revised:  Training of the social discrete choice models is performed using a specialized Monte Carlo expectation maximization (MCEM) algorithm.
Edit intent: clarity
Original:  We present and explain extensive experiments in which we demonstrate on which types of datasets our model is expected to outperform state-of-the-art models.
Revised:  We present and explain extensive experiments in which we demonstrate on which types of datasets our model can be expected to outperform state-of-the-art models.
Edit intent: clarity
Original:  We derive and analyse new mathematical models for the BR signalling pathway and  the crosstalk between the BR and GA signalling pathways.
Revised:  We derive and analyse new mathematical models for the BR signalling pathway and for the crosstalk between the BR and GA signalling pathways.
Edit intent: fluency
Original:  We show that solutions of our models can exhibit oscillatory behaviour depending on the parameters associated with BZR1/2 phosphorylation.
Revised:  The stability of steady state solutions of our models can exhibit oscillatory behaviour depending on the parameters associated with BZR1/2 phosphorylation.
Edit intent: clarity
Original: During asymmetric cell divisions, cortical dyneins generate forcesessential to position the spindle after polarity cues, prescribing daughter cells fate.
Revised: During asymmetric cell division, dynein generates forces, which position the spindle after polarity cues, prescribing daughter cells fate.
Edit intent: clarity
Original: A major challenge in network science is to determine whether an observed network property reveals some non-trivial behavior of the network's nodes , or if it is a consequence of the network 's elementary properties . Statistical null models serve this purpose by producing random networks whilst keeping chosen network's properties fixed.
Revised: A major challenge in network science is to determine whether an observed network property reveals some non-trivial pattern , or if it is a consequence of the network 's elementary properties . Statistical null models serve this purpose by producing random networks whilst keeping chosen network's properties fixed.
Edit intent: clarity
Original:  While there is increasing interest in networks that evolve in time, we still lack a robust time-aware framework to assess the statistical significance of the observed structural properties of growing networks .
Revised:  While there is increasing interest in networks that evolve in time, we still lack a robust time-aware framework to assess the statistical significance of their observed structural properties of growing networks .
Edit intent: clarity
Original:  While there is increasing interest in networks that evolve in time, we still lack a robust time-aware framework to assess the statistical significance of the observed structural properties of growing networks .
Revised:  While there is increasing interest in networks that evolve in time, we still lack a robust time-aware framework to assess the statistical significance of the observed structural properties .
Edit intent: clarity
Original:  We fill this gap by introducing a null model that, differently from  static models, preserves both the network's degree sequence and the  individual nodes' degree time-series .
Revised:  We fill this gap by introducing a null model that, differently from existing static models, preserves both the network's degree sequence and the individual nodes' degree time-series .
Edit intent: clarity
Original:  We fill this gap by introducing a null model that, differently from  static models, preserves both the network's degree sequence and the  individual nodes' degree time-series .
Revised:  We fill this gap by introducing a null model that, differently from static models, preserves both the network's degree sequence and the individual nodes' degree values .
Edit intent: clarity
Original:  By preserving the temporal linking patterns of the real systems it is applied to , the proposed model disentangles structural from temporal patterns.
Revised:  By preserving the temporal linking patterns of the analyzed system , the proposed model disentangles structural from temporal patterns.
Edit intent: clarity
Original:  By preserving the temporal linking patterns of the real systems it is applied to , the proposed model disentangles structural from temporal patterns.
Revised:  By preserving the temporal linking patterns of the real systems it is applied to , the proposed model is able to disentangle structural from temporal patterns.
Edit intent: clarity
Original: We analyze a family of portfolio management problems under relative performance criteria, for fund managers having CARA or CRRA utilities and trading in a common time horizon in log-normal markets.
Revised: We analyze a family of portfolio management problems under relative performance criteria, for fund managers having CARA or CRRA utilities and trading in a common investment horizon in log-normal markets.
Edit intent: clarity
Original: We introduce and study the game of  Selfish Cops and Adversarial Robber (SCAR) which is an N-player generalization of the classic two-player cops and robbers (CR) game.
Revised: We introduce and study the game of " Selfish Cops and Adversarial Robber (SCAR) which is an N-player generalization of the classic two-player cops and robbers (CR) game.
Edit intent: fluency
Original: We introduce and study the game of  Selfish Cops and Adversarial Robber (SCAR) which is an N-player generalization of the classic two-player cops and robbers (CR) game.
Revised: We introduce and study the game of Selfish Cops and Adversarial Robber (SCAR) which can be seen as an N-player generalization of the classic two-player cops and robbers (CR) game.
Edit intent: clarity
Original: We introduce and study the game of  Selfish Cops and Adversarial Robber (SCAR) which is an N-player generalization of the classic two-player cops and robbers (CR) game.
Revised: We introduce and study the game of Selfish Cops and Adversarial Robber (SCAR) which is an N-player variant of the "classic" two-player cops and robbers (CR) game.
Edit intent: clarity
Original: We introduce and study the game of  Selfish Cops and Adversarial Robber (SCAR) which is an N-player generalization of the classic two-player cops and robbers (CR) game.
Revised: We introduce and study the game of Selfish Cops and Adversarial Robber (SCAR) which is an N-player generalization of the classic two-player Cops and Robbers (CR) game.
Edit intent: fluency
Original:  We prove that SCAR has a Nash equilibrium in deterministic strategies  .
Revised:  We prove that SCAR always has Nash equilibria in deterministic strategies .
Edit intent: clarity
Original: We introduce and study the game of "Selfish Cops and Active Robber" (SCAR) which can be seen as an N-player variant of the "classic" two-player Cops and Robbers (CR) game.
Revised: We introduce and study the game of "Selfish Cops and Active Robber" (SCAR) which can be seen as an multiplayer variant of the "classic" two-player Cops and Robbers (CR) game.
Edit intent: clarity
Original:  Rational play is formulated in terms of Nash Equilibria (NE) and we prove that SCAR always has Nash equilibria in deterministic strategies and at least one of these involves only positional strategies .
Revised:  Rational play is formulated in terms of Nash Equilibria (NE) . In particular, we prove that SCAR always has Nash equilibria in deterministic strategies and at least one of these involves only positional strategies .
Edit intent: coherence
Original:  Rational play is formulated in terms of Nash Equilibria (NE) and we prove that SCAR always has Nash equilibria in deterministic strategies and at least one of these involves only positional strategies .
Revised:  Rational play is formulated in terms of Nash Equilibria (NE) and we prove that SCAR always has Nash equilibria in deterministic strategies .
Edit intent: coherence
Original:  we also define the selfish cop number of a graph and study its connections to the classic cop number.
Revised:  we also define the selfish cop number of a graph and study its connection to the classic cop number.
Edit intent: fluency
Original:  The methodology involves (i) data from fatigue tests conducted on coupons of Ti6Al4V material ;
Revised:  The methodology involves (i) utilization of fatigue tests data conducted on coupons of Ti6Al4V material ;
Edit intent: clarity
Original:  The methodology involves (i) data from fatigue tests conducted on coupons of Ti6Al4V material ;
Revised:  The methodology involves (i) data from fatigue tests conducted on coupons of Ti6Al4V material 
Edit intent: fluency
Original:  (ii) continuum damage mechanics based material constitutive models to simulate cyclic fatigue behavior of material ;
Revised:  (ii) continuum damage mechanics based material constitutive models to simulate cyclic fatigue behavior of material 
Edit intent: fluency
Original:  (iii) variance-based global sensitivity analysis ;
Revised:  (iii) variance-based global sensitivity analysis 
Edit intent: fluency
Original:  (iv) Bayesian framework for model calibration and uncertainty quantification ;
Revised:  (iv) Bayesian framework for model calibration and uncertainty quantification 
Edit intent: fluency
Original:  Moreover, using probabilistic design methods result in assessment of reliability of fatigue life predicted by computational models.
Revised:  Moreover, using probabilistic design meth- ods result in assessment of reliability of fatigue life predicted by computational models.
Edit intent: fluency
Original:  The methodology involves (i) utilization of fatigue tests data conducted on coupons of Ti6Al4V material (ii) continuum damage mechanics based material constitutive models to simulate cyclic fatigue behavior of material (iii) variance-based global sensitivity analysis (iv) Bayesian framework for model calibration and uncertainty quantification and (v) computational life prediction and probabilistic design decision making under uncertainty.
Revised:  The methodology involves (i) fatigue test data conducted on coupons of Ti6Al4V material (ii) continuum damage mechanics based material constitutive models to simulate cyclic fatigue behavior of material (iii) variance-based global sensitivity analysis (iv) Bayesian framework for model calibration and uncertainty quantification and (v) computational life prediction and probabilistic design decision making under uncertainty.
Edit intent: clarity
Original:  Moreover, using probabilistic design meth- ods result in assessment of reliability of fatigue life predicted by computational models.
Revised:  Moreover, using probabilistic design methods result in assessment of reliability of fatigue life predicted by computational models.
Edit intent: fluency
Original: Newton method is one of the most powerful methods for finding solution of nonlinear equations  .
Revised: Newton method is one of the most powerful methods for finding solutions of nonlinear equations .
Edit intent: fluency
Original:  The results are applied to systems of quadratic equations,  one-dimensional equations and inequalities.
Revised:  The results are specified for systems of quadratic equations, one-dimensional equations and inequalities.
Edit intent: clarity
Original: We define labeling homomorphisms on the cubical homology of higher-dimensional automata and show that they are natural with respect to cubical dimaps and compatible with tensor products .
Revised: We construct labeling homomorphisms on the cubical homology of higher-dimensional automata and show that they are natural with respect to cubical dimaps and compatible with tensor products .
Edit intent: clarity