wanyu/IteraTeR_v2 huggingface dataset:
Original:  there is an algorithm that approximates the function to within a factor O(log(1/epsilon)) on a set of measure 1-epsilon, for any epsilon > 0. ( 2) If we do not assume that the distribution is a product distribution, then the approximation factor must be much worse: no algorithm can approximate the function to within a factor of O~(n^{1/3 distributional learning and PAC-style analyses) and with central concepts in pseudo-randomness (lossless expander graphs).
Revised:  there is an algorithm that approximates the function to within a factor O(log(1/epsilon)) on a set of measure 1-epsilon, for any epsilon > 0. ( distributional learning and PAC-style analyses) and with central concepts in pseudo-randomness (lossless expander graphs).
Edit intent: coherence
Original: This paper describe the symmentry and asymmentry of TM and problems .
Revised: This paper talk about the complexity of computation by Turing Machine .
Edit intent: clarity
Original: The ongoing debate over "net neutrality " covers a broad set of issues related to the regulation of public networks.
Revised: The ongoing debate over net neutrality covers a broad set of issues related to the regulation of public networks.
Edit intent: fluency
Original:  This paper contains two separate contributions: (a) an extension of the quadratic-utility framework we proposed in a previous paper to study the impact of side payments in a system involving pluralities of access and content providers ;
Revised:  This paper contains two separate contributions: (a) an extension of the quadratic-utility framework we proposed in a previous paper to study the impact of "side payments" among a plurality of Internet service (access) providers and content providers ;
Edit intent: clarity
Original:  We start with recent negative results on quantum algorithms for Graph Isomorphism, which are based on particular subgroups of size two, and extend them to subgroups of arbitrary structure, including the automorphism groups of Goppa codes.
Revised:  We start with recent negative results on quantum algorithms for Graph Isomorphism, which are based on particular subgroups of size two, and extend them to subgroups of arbitrary structure, including the automorphism groups of linear codes.
Edit intent: clarity
Original:  DXNN utilizes a modular and hierarchicaltopology which promotes highly scalable and dynamically granular systems to evolve.
Revised:  DXNN utilizes a hierarchical/modular topology which allows for highly scalable and dynamically granular systems to evolve.
Edit intent: clarity
Original:  Among the novel features discussed in this paper is a simple and database friendly encoding for hierarchical/modular NNs, a new selection method aimed at producing highly compact and fit individuals within the population, and a new training phase referred to as " Tuning Phase " which is aimed at removing the need for speciation algorithms.
Revised:  Among the novel features discussed in this paper is a simple and database friendly encoding for hierarchical/modular NNs, a new selection method aimed at producing highly compact and fit individuals within the population, a " Tuning Phase " which is aimed at removing the need for speciation algorithms.
Edit intent: coherence
Original:  Among the novel features discussed in this paper is a simple and database friendly encoding for hierarchical/modular NNs, a new selection method aimed at producing highly compact and fit individuals within the population, and a new training phase referred to as " Tuning Phase " which is aimed at removing the need for speciation algorithms.
Revised:  Among the novel features discussed in this paper is a simple and database friendly encoding for hierarchical/modular NNs, a new selection method aimed at producing highly compact and fit individuals within the population, and a new training phase referred to as " Targeted Tunning " which is aimed at removing the need for speciation algorithms.
Edit intent: clarity
Original:  Mutation operators aimed at improving diversity , expandability, and capabilities of the DXNN through a built in feature selection method that allows for the evolved system to expand, discover  and explore new sensors and actuators is also covered.
Revised:  I will discuss DXNN's mutation operators which are aimed at improving diversity , expandability, and capabilities of the DXNN through a built in feature selection method that allows for the evolved system to expand, discover and explore new sensors and actuators is also covered.
Edit intent: clarity
Original:  Mutation operators aimed at improving diversity , expandability, and capabilities of the DXNN through a built in feature selection method that allows for the evolved system to expand, discover  and explore new sensors and actuators is also covered.
Revised:  Mutation operators aimed at improving diversity , expandability, and capabilities through a built in feature selection method that allows for the evolved system to expand, discover and explore new sensors and actuators is also covered.
Edit intent: clarity
Original:  Mutation operators aimed at improving diversity , expandability, and capabilities of the DXNN through a built in feature selection method that allows for the evolved system to expand, discover  and explore new sensors and actuators is also covered.
Revised:  Mutation operators aimed at improving diversity , expandability, and capabilities of the DXNN through a built in feature selection method that allows for the evolved system to expand, discover , and explore new sensors and actuators is also covered.
Edit intent: fluency
Original:  Finally , DXNN platform is then compared to other state of the art TWEANNs on a control task to demonstrate its  ability to produce highly compact solutions faster than its competitors.
Revised:  Finally , DXNN platform is then compared to other state of the art TWEANNs on a control task to demonstrate its superior ability to produce highly compact solutions faster than its competitors.
Edit intent: clarity
Original:  We prove that if L is closed and regular, then L-* is regular.
Revised:  It is known that if L is closed and regular, then L-* is regular.
Edit intent: coherence
Original:  Brain tumours are considered as fast-growth tumours because of their high rate of proliferation.
Revised:  Brain tumours are considered fast-growth tumours because of their high rate of proliferation.
Edit intent: fluency
Original:  In addition, tumour cells exhibit profound genetic, biochemical and histological differences with respect to the original non-transformed cellular types.
Revised:  In addition, tumour cells exhibit profound genetic, biochemical and histological differences with respect to the original non-transformed cell types.
Edit intent: fluency
Original:  Therefore, there is a strong interest from the clinical investigator  point of view in understanding the role of brain metabolites in normal and pathological conditions and especially on the development of early tumour detection techniques.
Revised:  Therefore, there is strong interest from the clinical investigator point of view in understanding the role of brain metabolites in normal and pathological conditions and especially on the development of early tumour detection techniques.
Edit intent: fluency
Original:  Therefore, there is a strong interest from the clinical investigator  point of view in understanding the role of brain metabolites in normal and pathological conditions and especially on the development of early tumour detection techniques.
Revised:  Therefore, there is a strong interest from the clinical investigator 's point of view in understanding the role of brain metabolites in normal and pathological conditions and especially on the development of early tumour detection techniques.
Edit intent: fluency
Original:  Therefore, there is a strong interest from the clinical investigator  point of view in understanding the role of brain metabolites in normal and pathological conditions and especially on the development of early tumour detection techniques.
Revised:  Therefore, there is a strong interest from the clinical investigator point of view in understanding the role of brain metabolites under normal and pathological conditions and especially on the development of early tumour detection techniques.
Edit intent: clarity
Original:  Therefore, there is a strong interest from the clinical investigator  point of view in understanding the role of brain metabolites in normal and pathological conditions and especially on the development of early tumour detection techniques.
Revised:  Therefore, there is a strong interest from the clinical investigator point of view in understanding the role of brain metabolites in normal and pathological conditions and especially in the development of early tumour detection techniques.
Edit intent: coherence
Original:  It is largely believed that temporal variations of NMR Spectra are noisy or just simply do not carry enough information to be exploited by any reliable diagnosis procedure.
Revised:  It is largely believed that temporal variations of NMR Spectra are simply due to noise or do not carry enough information to be exploited by any reliable diagnosis procedure.
Edit intent: clarity
Original:  In this paper, we firstly introduce a machine learning framework for the analysis of NMR spectroscopy signals that is able to exploit both static and dynamic aspects of these signals  . Secondly, the dynamics of these signals are further analyzed using elements from chaos theory aimed at understanding their underlying structure.
Revised:  In this paper, firstly a machine learning framework for the analysis of NMR spectroscopy signals that is able to exploit both static and dynamic aspects of these signals . Secondly, the dynamics of these signals are further analyzed using elements from chaos theory aimed at understanding their underlying structure.
Edit intent: coherence
Original:  In this paper, we firstly introduce a machine learning framework for the analysis of NMR spectroscopy signals that is able to exploit both static and dynamic aspects of these signals  . Secondly, the dynamics of these signals are further analyzed using elements from chaos theory aimed at understanding their underlying structure.
Revised:  In this paper, we firstly introduce a machine learning framework for the analysis of NMR spectroscopy signals which can exploit both static and dynamic aspects of these signals . Secondly, the dynamics of these signals are further analyzed using elements from chaos theory aimed at understanding their underlying structure.
Edit intent: clarity
Original:  In this paper, we firstly introduce a machine learning framework for the analysis of NMR spectroscopy signals that is able to exploit both static and dynamic aspects of these signals  . Secondly, the dynamics of these signals are further analyzed using elements from chaos theory aimed at understanding their underlying structure.
Revised:  In this paper, we firstly introduce a machine learning framework for the analysis of NMR spectroscopy signals that is able to exploit both static and dynamic aspects of these signals is introduced . Secondly, the dynamics of these signals are further analyzed using elements from chaos theory aimed at understanding their underlying structure.
Edit intent: coherence
Original:  In this paper, we firstly introduce a machine learning framework for the analysis of NMR spectroscopy signals that is able to exploit both static and dynamic aspects of these signals  . Secondly, the dynamics of these signals are further analyzed using elements from chaos theory aimed at understanding their underlying structure.
Revised:  In this paper, we firstly introduce a machine learning framework for the analysis of NMR spectroscopy signals that is able to exploit both static and dynamic aspects of these signals . Secondly, the dynamics of the signals are further analyzed using elements from chaos theory aimed at understanding their underlying structure.
Edit intent: fluency
Original:  In this paper, we firstly introduce a machine learning framework for the analysis of NMR spectroscopy signals that is able to exploit both static and dynamic aspects of these signals  . Secondly, the dynamics of these signals are further analyzed using elements from chaos theory aimed at understanding their underlying structure.
Revised:  In this paper, we firstly introduce a machine learning framework for the analysis of NMR spectroscopy signals that is able to exploit both static and dynamic aspects of these signals . Secondly, the dynamics of these signals are further analyzed using elements from chaos theory in order to understand their underlying structure.
Edit intent: coherence
Original:  Furthermore, we show that they exhibit rich chaotic dynamics suggesting the encoding of metabolic pathways information.
Revised:  Furthermore, we show that they exhibit rich chaotic dynamics suggesting the encoding of metabolic pathway information.
Edit intent: fluency
Original:  We consider the graphs these relations induce and we perform a random walk on the union multigraphof these graphs .
Revised:  We consider the graphs these relations induce , by performing a random walk on the union multigraphof these graphs .
Edit intent: coherence
Original:  We consider the graphs these relations induce and we perform a random walk on the union multigraphof these graphs .
Revised:  We consider the graphs these relations induce and we perform a random walk on their union multigraph .
Edit intent: clarity
Original:  We demonstrate the benefits of our approach through (i) simulation in synthetic graphs  and (ii) measurements of Last.fm - an Internet website for music with social networking features.
Revised:  We demonstrate the benefits of our approach through (i) simulation in synthetic graphs , and (ii) measurements of Last.fm - an Internet website for music with social networking features.
Edit intent: fluency
Original: We determine the complexity of approximate counting of the total weight of assignments for complex-weighted Boolean constraint satisfaction problems (or CSPs) , particularly, when degrees of  instances are bounded from above by a given constant, provided that all arity-1 constraints are freely available .
Revised: We determine the computational complexity of approximately counting the total weight of assignments for complex-weighted Boolean constraint satisfaction problems (or CSPs) , particularly, when degrees of instances are bounded from above by a given constant, provided that all arity-1 constraints are freely available .
Edit intent: clarity
Original: We determine the complexity of approximate counting of the total weight of assignments for complex-weighted Boolean constraint satisfaction problems (or CSPs) , particularly, when degrees of  instances are bounded from above by a given constant, provided that all arity-1 constraints are freely available .
Revised: We determine the complexity of approximate counting of the total weight of assignments for complex-weighted Boolean constraint satisfaction problems (or CSPs) , particularly, when degrees of input instances are bounded from above by a given constant, provided that all arity-1 constraints are freely available .
Edit intent: clarity
Original: We determine the complexity of approximate counting of the total weight of assignments for complex-weighted Boolean constraint satisfaction problems (or CSPs) , particularly, when degrees of  instances are bounded from above by a given constant, provided that all arity-1 constraints are freely available .
Revised: We determine the complexity of approximate counting of the total weight of assignments for complex-weighted Boolean constraint satisfaction problems (or CSPs) , particularly, when degrees of instances are bounded from above by a fixed constant .
Edit intent: clarity
Original:  All degree-1 counting CSPs are  solvable in polynomial time.
Revised:  All degree-1 counting CSPs are obviously solvable in polynomial time.
Edit intent: coherence
Original:  When the  degree is more than 2, we present a trichotomy theorem that classifies all bounded-degree counting CSPs into only three categories with a help of free arity-1 constraints .
Revised:  When the degree is more than 2, we present a trichotomy theorem that classifies all counting CSPs with free unary constraints into exactly three categories .
Edit intent: clarity
Original:  This classification extends to complex-weighted problems  an earlier result of Dyer, Goldberg, Jalsenius, and Richerby (2010)
Revised:  This classification theorem extends, to complex-weighted problems an earlier result of Dyer, Goldberg, Jalsenius, and Richerby (2010)
Edit intent: clarity
Original:  This classification extends to complex-weighted problems  an earlier result of Dyer, Goldberg, Jalsenius, and Richerby (2010)
Revised:  This classification extends to complex-weighted problems , an earlier result of Dyer, Goldberg, Jalsenius, and Richerby (2010)
Edit intent: fluency
Original:  on the complexity of the approximate counting of bounded-degree unweighted Boolean CSPs . The framework of the proof of our trichotomy theorem is based on a theory of signatures (Cai and Lu, 2007, 2008) used in Valiant's holographic algorithms  . Despite the use of arbitrary complex-weight, our proof is rather elementary and intuitive by an extensive use of a  notion of limited T-constructibility.
Revised:  on the complexity of the approximate counting of bounded-degree unweighted Boolean CSPs . The framework of the proof of our theorem is based on a theory of signatures (Cai and Lu, 2007, 2008) used in Valiant's holographic algorithms . Despite the use of arbitrary complex-weight, our proof is rather elementary and intuitive by an extensive use of a notion of limited T-constructibility.
Edit intent: clarity
Original:  on the complexity of the approximate counting of bounded-degree unweighted Boolean CSPs . The framework of the proof of our trichotomy theorem is based on a theory of signatures (Cai and Lu, 2007, 2008) used in Valiant's holographic algorithms  . Despite the use of arbitrary complex-weight, our proof is rather elementary and intuitive by an extensive use of a  notion of limited T-constructibility.
Revised:  on the complexity of the approximate counting of bounded-degree unweighted Boolean CSPs . The framework of the proof of our trichotomy theorem is based on a theory of signatures developed from Valiant's holographic algorithms . Despite the use of arbitrary complex-weight, our proof is rather elementary and intuitive by an extensive use of a notion of limited T-constructibility.
Edit intent: clarity
Original:  on the complexity of the approximate counting of bounded-degree unweighted Boolean CSPs . The framework of the proof of our trichotomy theorem is based on a theory of signatures (Cai and Lu, 2007, 2008) used in Valiant's holographic algorithms  . Despite the use of arbitrary complex-weight, our proof is rather elementary and intuitive by an extensive use of a  notion of limited T-constructibility.
Revised:  on the complexity of the approximate counting of bounded-degree unweighted Boolean CSPs . The framework of the proof of our trichotomy theorem is based on a theory of signatures (Cai and Lu, 2007, 2008) used in Valiant's holographic algorithms . Despite the use of arbitrary complex-weight, our proof is rather elementary and intuitive due to an extensive use of a notion of limited T-constructibility.
Edit intent: coherence
Original:  on the complexity of the approximate counting of bounded-degree unweighted Boolean CSPs . The framework of the proof of our trichotomy theorem is based on a theory of signatures (Cai and Lu, 2007, 2008) used in Valiant's holographic algorithms  . Despite the use of arbitrary complex-weight, our proof is rather elementary and intuitive by an extensive use of a  notion of limited T-constructibility.
Revised:  on the complexity of the approximate counting of bounded-degree unweighted Boolean CSPs . The framework of the proof of our trichotomy theorem is based on a theory of signatures (Cai and Lu, 2007, 2008) used in Valiant's holographic algorithms . Despite the use of arbitrary complex-weight, our proof is rather elementary and intuitive by an extensive use of a novel notion of limited T-constructibility.
Edit intent: clarity
Original:  For the  degree-2 problems,  we show that they are as hard to approximate as complex Holant problems .
Revised:  For the degree-2 problems, in contrast, we show that they are as hard to approximate as complex Holant problems .
Edit intent: coherence
Original:  When the instance  degree is more than 2 , we present a trichotomy theorem that classifies all counting CSPs with free unary constraints into exactly three categories.
Revised:  When the instance 's degree is more than 2 , we present a trichotomy theorem that classifies all counting CSPs with free unary constraints into exactly three categories.
Edit intent: fluency
Original:  When the instance  degree is more than 2 , we present a trichotomy theorem that classifies all counting CSPs with free unary constraints into exactly three categories.
Revised:  When the instance degree is more than two , we present a trichotomy theorem that classifies all counting CSPs with free unary constraints into exactly three categories.
Edit intent: fluency
Original:  When the instance  degree is more than 2 , we present a trichotomy theorem that classifies all counting CSPs with free unary constraints into exactly three categories.
Revised:  When the instance degree is more than 2 , we present a dichotomy theorem that classifies all counting CSPs with free unary constraints into exactly three categories.
Edit intent: fluency
Original:  When the instance  degree is more than 2 , we present a trichotomy theorem that classifies all counting CSPs with free unary constraints into exactly three categories.
Revised:  When the instance degree is more than 2 , we present a trichotomy theorem that classifies all counting CSPs admitting free unary constraints into exactly three categories.
Edit intent: fluency
Original:  The framework of the proof of our theorem is based on a theory of signatures developed from Valiant's holographic algorithms that can efficiently solve seemingly intractable counting CSPs.
Revised:  The framework of the proof of our theorem is based on a theory of signature developed from Valiant's holographic algorithms that can efficiently solve seemingly intractable counting CSPs.
Edit intent: fluency
Original:  Despite the use of arbitrary complex-weight , our proof  is rather elementary and intuitive due to an extensive use of a novel notion of limited T-constructibility.
Revised:  Despite the use of arbitrary complex weight , our proof is rather elementary and intuitive due to an extensive use of a novel notion of limited T-constructibility.
Edit intent: fluency
Original:  For the remaining degree-2 problems, in contrast, we show that they are as hard to approximate as Holant problems, which are a generalization of counting CSPs.
Revised:  For the remaining degree-2 problems, in contrast, they are as hard to approximate as Holant problems, which are a generalization of counting CSPs.
Edit intent: coherence
Original:  We  show that, though the solutions of the deterministic mean-field equation constitute uncorrelated solutions of the new mean-field equations, the stability properties of limit cycles are modified by the presence of correlations, and additional non-trivial behaviors including periodic orbits appear when there were none in the mean fileld .
Revised:  We show that, though the solutions of the deterministic mean-field equation constitute uncorrelated solutions of the new mean-field equations, the stability properties of limit cycles are modified by the presence of correlations, and additional non-trivial behaviors including periodic orbits appear when there were none in the mean field .
Edit intent: clarity