wanyu/IteraTeR_v2 huggingface dataset:
Original:  Our implementation produces accurate counter-examples when properties are violated and  in the extreme case , with sufficient problem structure, is shown to be able to analyze a system with a billion real-valued state variables.
Revised:  Our implementation produces accurate counter-examples when properties are violated and in the extreme case , with sufficient problem structure, is shown to be able to analyze a system with one billion real-valued state variables.
Edit intent: fluency
Original: The pigeonhole principle states that if n items are contained in m boxes, then at least one box has no fewer than n/m items.
Revised: The pigeonhole principle states that if n items are contained in m boxes, then at least one box has no more than n/m items.
Edit intent: clarity
Original:  We propose a new principle  called the pigeonring principle which formally captures such constraints and yields stronger conditions.
Revised:  We propose a new principle , called the pigeonring principle which formally captures such constraints and yields stronger conditions.
Edit intent: fluency
Original:  To utilize the pigeonring principle, we focus on problems defined in the form of identifying data objects whose similarities or distances to the query is constrained by a threshold.
Revised:  To utilize the new principle, we focus on problems defined in the form of identifying data objects whose similarities or distances to the query is constrained by a threshold.
Edit intent: clarity
Original:  By the pigeonring principle, stronger filtering conditions can be established.
Revised:  By the new principle, stronger filtering conditions can be established.
Edit intent: clarity
Original:  This suggests that all the solutions based on the pigeonhole principle are possible to be accelerated by the pigeonring principle.
Revised:  This suggests that all the pigeonhole principle-based solutions are possible to be accelerated by the pigeonring principle.
Edit intent: fluency
Original:  This suggests that all the solutions based on the pigeonhole principle are possible to be accelerated by the pigeonring principle.
Revised:  This suggests that all the solutions based on the pigeonhole principle are possible to be accelerated by the new principle.
Edit intent: clarity
Original:  A universal filtering framework is introduced to encompass the solutions to these problems based on the pigeonring principle.
Revised:  A universal filtering framework is introduced to encompass the solutions to these problems based on the new principle.
Edit intent: clarity
Original:  Besides, we discuss how to quickly find candidates specified by the pigeonring principlewith minor modifications on top of existing  algorithms.
Revised:  Besides, we discuss how to quickly find candidates specified by the pigeonring principlewith minor modifications on top of existing pigeonhole principle-based algorithms.
Edit intent: clarity
Original:  This paper then summarizes deep learning's applications in many areas of artificial intelligence, including voice , computer vision, natural language processing and so on.
Revised:  This paper then summarizes deep learning's applications in many areas of artificial intelligence, including speech processing , computer vision, natural language processing and so on.
Edit intent: clarity
Original:  Our work is the first to study audio source separation in large-scale general "in the wild" videos  .
Revised:  Our work is the first to learn audio source separation in large-scale general "in the wild" videos .
Edit intent: clarity
Original:  Our work is the first to study audio source separation in large-scale general "in the wild" videos  .
Revised:  Our work is the first to study audio source separation from large-scale general "in the wild" videos .
Edit intent: clarity
Original:  Our work is the first to study audio source separation in large-scale general "in the wild" videos  .
Revised:  Our work is the first to study audio source separation in large-scale "in the wild" videos .
Edit intent: clarity
Original: The  Stieltjes constants \gamma\_n are the coefficients appearing in the Laurent series of the Riemann zeta function at s = 1. We give a simple and efficient method to compute a p-bit approximation of \gamma\_n with rigorous error bounds . Starting from an integral representation due to Blagouchine, we shift the contour to eliminate cancellation.
Revised: The Stieltjes constants \gamma\_n are the coefficients appearing in the Laurent series of the Riemann zeta function at s = 1. In this work, we devise an efficient algorithm to compute these constants to arbitrary precision with rigorous error bounds . Starting from an integral representation due to Blagouchine, we shift the contour to eliminate cancellation.
Edit intent: clarity
Original:  The integral is then evaluated numerically in ball arithmetic using the Petras algorithm , with the use of a Taylor expansion for bounds near the saddle point.
Revised:  The integral is then evaluated numerically in ball arithmetic using the Petras algorithm with a Taylor expansion for bounds near the saddle point.
Edit intent: coherence
Original:  This appears to be the first algorithm for Stieltjes constants with uniformly low complexity with respect to both n and p. An implementation is provided in the Arb library.
Revised:  An implementation is provided in the Arb library.
Edit intent: coherence
Original:  We can, for example, compute \gamma\_n  to 1000 digits in a minute for any n %DIFDELCMD < \le %%%  10^{100}  .
Revised:  We can, for example, compute \gamma\_n to 1000 digits in a minute for any n %DIFDELCMD < \le %%% up to n= 10^{100} .
Edit intent: clarity
Original: As two most prevalent microscopic mechanisms of strategy spreading, frequency-dependent Moran process and pairwise comparison process are widely used to model population traits' evolution in evolutionary game dynamics .
Revised: In the most studies regarding evolutionary game dynamics .
Edit intent: clarity
Original:  Thus, irrespective of the scaling factor, any two } fitness or imitation probability functions are equivalent under weak selection.
Revised:  Thus, irrespective of the scaling factor, any two } fitness or imitation mappings are equivalent under weak selection.
Edit intent: clarity
Original:  In the meanwhile , the effect of different effective payoff functions on evolutionary dynamics is always left in the basket.
Revised:  Meanwhile , the effect of different effective payoff functions on evolutionary dynamics is always left in the basket.
Edit intent: coherence
Original:  In the meanwhile , the effect of different effective payoff functions on evolutionary dynamics is always left in the basket.
Revised:  In the meanwhile , the effect of different function forms of effective payoff on evolutionary dynamics is always left in the basket.
Edit intent: clarity
Original: In the most studies regarding evolutionary game dynamics, the effective payoff, a quantity that translates the payoff derived from game interactions into reproductive success, is usually assumed to be a specific function of the payoff.
Revised: In most studies regarding evolutionary game dynamics, the effective payoff, a quantity that translates the payoff derived from game interactions into reproductive success, is usually assumed to be a specific function of the payoff.
Edit intent: fluency
Original:  Taking  Moran process and pairwise comparison process as specific models in well-mixed populations, we find that different fitness or imitation mappings are equivalent under weak selection.
Revised:  Taking the Moran process and pairwise comparison process as specific models in well-mixed populations, we find that different fitness or imitation mappings are equivalent under weak selection.
Edit intent: fluency
Original:  This work thus helps to elucidate how the effective payoff functions as another fundamental ingredient of evolution affect evolutionary dynamics.
Revised:  This work thus helps to elucidate how the effective payoff function as another fundamental ingredient of evolution affect evolutionary dynamics.
Edit intent: fluency
Original: We consider weighted particle systems of fixed size, in which a new generation of particles is formed by resampling particles from the current generation with probabilities proportional to their weights.
Revised: We study weighted particle systems of fixed size, in which a new generation of particles is formed by resampling particles from the current generation with probabilities proportional to their weights.
Edit intent: fluency
Original: We consider weighted particle systems of fixed size, in which a new generation of particles is formed by resampling particles from the current generation with probabilities proportional to their weights.
Revised: We consider weighted particle systems in which new generations are resampled from current particles with probabilities proportional to their weights.
Edit intent: clarity
Original:  This set-up covers a broad class of sequential Monte Carlo (SMC) methods, which are widely-used in applied statistics and cognate disciplines across a range of domains .
Revised:  This covers a broad class of sequential Monte Carlo (SMC) methods, which are widely-used in applied statistics and cognate disciplines across a range of domains .
Edit intent: clarity
Original:  This set-up covers a broad class of sequential Monte Carlo (SMC) methods, which are widely-used in applied statistics and cognate disciplines across a range of domains .
Revised:  This set-up covers a broad class of sequential Monte Carlo (SMC) methods, widely-used in applied statistics and cognate disciplines across a range of domains .
Edit intent: coherence
Original:  This set-up covers a broad class of sequential Monte Carlo (SMC) methods, which are widely-used in applied statistics and cognate disciplines across a range of domains .
Revised:  This set-up covers a broad class of sequential Monte Carlo (SMC) methods, which are widely-used in applied statistics and cognate disciplines .
Edit intent: clarity
Original:  We consider the genealogical tree embedded into such particle systems by the resampling operation , and identify conditions, as well as an appropriate time-scaling, under which it converges to the Kingman coalescent in the infinite system size limit in the sense of finite-dimensional distributions.
Revised:  We consider the genealogical tree embedded into such particle systems , and identify conditions, as well as an appropriate time-scaling, under which it converges to the Kingman coalescent in the infinite system size limit in the sense of finite-dimensional distributions.
Edit intent: coherence
Original:  We consider the genealogical tree embedded into such particle systems by the resampling operation , and identify conditions, as well as an appropriate time-scaling, under which it converges to the Kingman coalescent in the infinite system size limit in the sense of finite-dimensional distributions.
Revised:  We consider the genealogical tree embedded into such particle systems by the resampling operation , and identify conditions, as well as an appropriate time-scaling, under which they converge to the Kingman coalescent in the infinite system size limit in the sense of finite-dimensional distributions.
Edit intent: fluency
Original:  This makes the plethora of distributional results known for the Kingman coalescent available for analysis of SMC algorithms, which we illustrate by characterising the limiting mean and variance of the tree height , as well as of the total branch length of the tree.
Revised:  Thus, the tractable n-coalescent can be used to predict the shape and size of SMC genealogies, as we illustrate by characterising the limiting mean and variance of the tree height , as well as of the total branch length of the tree.
Edit intent: clarity
Original:  The conditions which we require to prove convergence are strong, but we demonstrate by simulation that they do not appear to be necessary.
Revised:  The conditions which we require to prove convergence are strong, but we show by simulation that they do not appear to be necessary.
Edit intent: fluency
Original:  From a combinatorial point of view, such networks are certain types of rooted directed acyclic graphs whose of leaves are labelled by, for example, species.
Revised:  From a combinatorial point of view, such networks are certain types of rooted directed acyclic graphs whose leaves are labelled by, for example, species.
Edit intent: fluency
Original:  These include the biologically relevant class of stable phylogenetic networks whose members are defined via certain " fold-up " and " un-fold " operations that link them with concepts arising within the theory of, for example, graph fibrations.
Revised:  These include the biologically relevant class of stable phylogenetic networks whose members are defined via certain fold-up " and " un-fold " operations that link them with concepts arising within the theory of, for example, graph fibrations.
Edit intent: fluency
Original:  These include the biologically relevant class of stable phylogenetic networks whose members are defined via certain " fold-up " and " un-fold " operations that link them with concepts arising within the theory of, for example, graph fibrations.
Revised:  These include the biologically relevant class of stable phylogenetic networks whose members are defined via certain " fold-up and un-fold " operations that link them with concepts arising within the theory of, for example, graph fibrations.
Edit intent: fluency
Original:  These include the biologically relevant class of stable phylogenetic networks whose members are defined via certain " fold-up " and " un-fold " operations that link them with concepts arising within the theory of, for example, graph fibrations.
Revised:  These include the biologically relevant class of stable phylogenetic networks whose members are defined via certain " fold-up " and " un-fold operations that link them with concepts arising within the theory of, for example, graph fibrations.
Edit intent: fluency
Original:  Employing the popular tree-based, reticulation-visible, and tree-child properties which allow one to gauge this complexity in one way or another, we provide novel characterizations of when a stable phylogenetic network satisfies either one of these three properties.
Revised:  Employing the popular tree-based, reticulation-visible, and tree-child properties which allow one to gauge this complexity in one way or another, we provide novel characterizations for when a stable phylogenetic network satisfies either one of these three properties.
Edit intent: fluency
Original:  These include the biologically relevant class of stable phylogenetic networks whose members are defined via certain  fold-up and un-fold  operations that link them with concepts arising within the theory of, for example, graph fibrations.
Revised:  These include the biologically relevant class of stable phylogenetic networks whose members are defined via certain " fold-up and un-fold operations that link them with concepts arising within the theory of, for example, graph fibrations.
Edit intent: fluency
Original:  These include the biologically relevant class of stable phylogenetic networks whose members are defined via certain  fold-up and un-fold  operations that link them with concepts arising within the theory of, for example, graph fibrations.
Revised:  These include the biologically relevant class of stable phylogenetic networks whose members are defined via certain fold-up " and " un-fold operations that link them with concepts arising within the theory of, for example, graph fibrations.
Edit intent: fluency
Original:  These include the biologically relevant class of stable phylogenetic networks whose members are defined via certain  fold-up and un-fold  operations that link them with concepts arising within the theory of, for example, graph fibrations.
Revised:  These include the biologically relevant class of stable phylogenetic networks whose members are defined via certain fold-up and un-fold " operations that link them with concepts arising within the theory of, for example, graph fibrations.
Edit intent: fluency
Original:  Two of the most popular approaches for community detection are maximizing an objective function called "modularity" and performing statistical inference using stochastic block models.
Revised:  Two of the most popular approaches for community detection are to maximize an objective function called "modularity" and performing statistical inference using stochastic block models.
Edit intent: fluency
Original:  Two of the most popular approaches for community detection are maximizing an objective function called "modularity" and performing statistical inference using stochastic block models.
Revised:  Two of the most popular approaches for community detection are maximizing an objective function called "modularity" and to perform statistical inference using stochastic block models.
Edit intent: fluency
Original:  Generalizing work by Newman on monolayer networks (Physical Review E 94, 052315), we show in multilayer networks that maximizing modularity is equivalent, under certain conditions, to maximizing the posterior probability of community assignments under  suitably chosen stochastic block models .
Revised:  Generalizing work by Newman on monolayer networks (Physical Review E 94, 052315), we show in multilayer networks that maximizing modularity is equivalent, under certain conditions, to maximizing the posterior probability of community assignments under a suitably chosen stochastic block models .
Edit intent: fluency
Original:  Generalizing work by Newman on monolayer networks (Physical Review E 94, 052315), we show in multilayer networks that maximizing modularity is equivalent, under certain conditions, to maximizing the posterior probability of community assignments under  suitably chosen stochastic block models .
Revised:  Generalizing work by Newman on monolayer networks (Physical Review E 94, 052315), we show in multilayer networks that maximizing modularity is equivalent, under certain conditions, to maximizing the posterior probability of community assignments under suitably chosen stochastic block model .
Edit intent: fluency
Original:  We derive versions of this equivalence for various types of multilayer structure, including temporal, multiplex, and multilevel (i.e., hierarchical) networks.
Revised:  We derive versions of this equivalence for various types of multilayer structure, including temporal, multiplex, and multilevel networks.
Edit intent: clarity
Original:  We consider cases in which the key parameters are constant  as well as ones in which they vary across layers;
Revised:  We consider cases in which the key parameters are constant , as well as ones in which they vary across layers;
Edit intent: fluency
Original:  A consequence of this theorem is that a function can be approximated on vertices of the box using other vertices to higher degrees than expected.
Revised:  A consequence of this fact is that a function can be approximated on vertices of the box using other vertices to higher degrees than expected.
Edit intent: clarity
Original:  In this paper, we present a first systematic mapping study of source code augmentation approaches and tools .
Revised:  In this paper, we present a first systematic mapping study of source code editor augmentation tools and approaches .
Edit intent: clarity
Original:  The result is a list of 103 relevant articles and a taxonomy of source code augmentation approaches with seven dimensions, which we used to categorize the resulting list of the surveyed articles.
Revised:  The result is a list of 103 relevant articles and a taxonomy of source code editor augmentation tools with seven dimensions, which we used to categorize the resulting list of the surveyed articles.
Edit intent: clarity
Original:  We also provide the definition of the term source code  augmentation, along with a brief overview of historical development and augmentations available in current industrial IDEs.
Revised:  We also provide the definition of the term source code editor augmentation, along with a brief overview of historical development and augmentations available in current industrial IDEs.
Edit intent: clarity
Original:  The characteristics of the approach and more than 5 thousand generated topics are described in detail.
Revised:  The characteristics of the approach with more than 5 thousand generated topics are described in detail.
Edit intent: fluency
Original:  Furthermore, they are compared with topics generated from the same datasets from an approach that produces human readable topics from micrblog post collections.
Revised:  Furthermore, they are compared with topics generated from the same datasets from an approach that produces human readable topics from microblog post collections.
Edit intent: fluency
Original: The Moran process is a randomised algorithm that models the spread of genetic mutations through graphs.
Revised: The Moran process is a random process that models the spread of genetic mutations through graphs.
Edit intent: clarity
Original:  Our main result is an almost-tight bound on the expected running timeof the algorithm .
Revised:  Our main result is an almost-tight bound on expected absorption time .
Edit intent: clarity
Original:  We show that no similar phase transition occurs for digraphs, where it is already known that the expected running time can also be exponential.
Revised:  We show that no similar phase transition occurs for digraphs, where it is already known that the expected absorption time can also be exponential.
Edit intent: clarity
Original: In this work , we associate the idea of derivation languages with at splicing systems and compare the languages generated as derivation languages (Szilard and Control languages) with the family of languages in Chomsky hierarchy.
Revised: In this paper , we associate the idea of derivation languages with at splicing systems and compare the languages generated as derivation languages (Szilard and Control languages) with the family of languages in Chomsky hierarchy.
Edit intent: clarity
Original: In this work , we associate the idea of derivation languages with at splicing systems and compare the languages generated as derivation languages (Szilard and Control languages) with the family of languages in Chomsky hierarchy.
Revised: In this work , we associate the idea of derivation languages with flat splicing systems and compare the languages generated as derivation languages (Szilard and Control languages) with the family of languages in Chomsky hierarchy.
Edit intent: fluency
Original: In this work , we associate the idea of derivation languages with at splicing systems and compare the languages generated as derivation languages (Szilard and Control languages) with the family of languages in Chomsky hierarchy.
Revised: In this work , we associate the idea of derivation languages with at splicing systems and compare the families of derivation languages (Szilard and Control languages) with the family of languages in Chomsky hierarchy.
Edit intent: clarity
Original:  Also, it is decidable whether or not SZ_{n, FIN}^{m}(LS) \subseteq R and R \subseteq SZ_{n, FIN}^{m}(LS) for any regular language R and labeled flat finite splicing system LS} . Also, any regular, context-free and recursively enumerable language can be represented as a homomorphic image of the Szilard language generated by the labeled flat  splicing systems of type (1, 2) ;
Revised:  Also, it is decidable whether or not SZ_{n, FIN}^{m}(LS) \subseteq R and R \subseteq SZ_{n, FIN}^{m}(LS) for any regular language R and labeled flat finite splicing system LS} . Also, any regular, context-free and recursively enumerable language can be obtained as homomorphic image of the Szilard language generated by the labeled flat splicing systems of type (1, 2) ;
Edit intent: clarity