wanyu/IteraTeR_v2 huggingface dataset:
Original:  In applications, computing Frechet means is probably most needed in the tree space, which is an instance of Hadamard spaces , invented by Billera, Holmes, and Vogtmann (2001) as a tool for averaging phylogenetic trees.
Revised:  In applications, computing Frechet means is probably most needed in tree space, which is an instance of Hadamard spaces , invented by Billera, Holmes, and Vogtmann (2001) as a tool for averaging phylogenetic trees.
Edit intent: fluency
Original:  In applications, computing Frechet means is probably most needed in the tree space, which is an instance of Hadamard spaces , invented by Billera, Holmes, and Vogtmann (2001) as a tool for averaging phylogenetic trees.
Revised:  In applications, computing Frechet means is probably most needed in the tree space, which is an instance of an Hadamard space , invented by Billera, Holmes, and Vogtmann (2001) as a tool for averaging phylogenetic trees.
Edit intent: clarity
Original:  It turns out, however, that it can also be used to model numerous other tree-like structures.
Revised:  It turns out, however, that it can be also used to model numerous other tree-like structures.
Edit intent: fluency
Original:  Since there now exists a polynomial-time algorithm for computing geodesics in the tree space due to Owen and Provan (2011), we obtain an efficient algorithm for computing Frechet means, which can be directly used in practice.
Revised:  Since there now exists a polynomial-time algorithm for computing geodesics in tree space due to Owen and Provan (2011), we obtain an efficient algorithm for computing Frechet means, which can be directly used in practice.
Edit intent: fluency
Original:  Since there now exists a polynomial-time algorithm for computing geodesics in the tree space due to Owen and Provan (2011), we obtain an efficient algorithm for computing Frechet means, which can be directly used in practice.
Revised:  Since there now exists a polynomial-time algorithm for computing geodesics in the tree space due to M. Owen and S. Provan (2011), we obtain an efficient algorithm for computing Frechet means, which can be directly used in practice.
Edit intent: clarity
Original:  When two binary matrices are disjoint is defined .
Revised:  It defines when two binary matrices are disjoint is defined .
Edit intent: clarity
Original:  When two binary matrices are disjoint is defined .
Revised:  When two binary matrices are disjoint .
Edit intent: clarity
Original:  For an arbitrary n^2 \times n^2 S-permutation matrix,  the number of all disjoint whit it S-permutation matrices is found.
Revised:  For an arbitrary n^2 \times n^2 S-permutation matrix, the number of all disjoint with it S-permutation matrices is found.
Edit intent: fluency
Original:   In particular, a new shorter proof of a known equality is obtained in the work  .
Revised:  In particular, a different proof of a known equality is obtained in the work .
Edit intent: clarity
Original:   In particular, a new shorter proof of a known equality is obtained in the work  .
Revised:  In particular, a new shorter proof of a known assertion is obtained in the work .
Edit intent: clarity
Original:  such a set has been called a finite-valued constraint language.
Revised:  such a set is called a finite-valued constraint language.
Edit intent: clarity
Original:  The valued constraint satisfaction problem, VCSP(Gamma), is the problem of minimising functions given as a sum of functions from Gamma.
Revised:  The valued constraint satisfaction problem, VCSP(Gamma), is the problem of minimising a function given as a sum of functions from Gamma.
Edit intent: fluency
Original:  The proof idea uses a variation of Motzkin's Transposition Theorem, hyperplane arrangements, and a technique recently introduced by Kolmogorov [arXiv:1207.7213] reformulated using Markov chains.
Revised:  The proof uses a variation of Motzkin's Transposition Theorem, hyperplane arrangements, and a technique recently introduced by Kolmogorov [arXiv:1207.7213] reformulated using Markov chains.
Edit intent: clarity
Original:  Our results generalise all previous partial classifications of finite-valued languages: the classifications of {0,1}-valued languages on two-element, three-element, and four-element domains obtained by Creignou [JCSS'95 , Jonsson et al.
Revised:  Our results generalise all previous partial classifications of finite-valued languages: the classifications of {0,1}-valued languages on two-element, three-element, and four-element domains obtained by Creignou [JCSS'95 ,
Edit intent: clarity
Original:  SICOMP'06 , and Jonsson et al.
Revised:  SICOMP'06 ,
Edit intent: coherence
Original:  CP'11] , respectively, the classification of {0,1}-valued languages containing all unary functions obtained by Deineko et al.
Revised:  CP'11] ; the classification of {0,1}-valued languages containing all unary functions obtained by Deineko et al.
Edit intent: coherence
Original:  CP'11] , respectively, the classification of {0,1}-valued languages containing all unary functions obtained by Deineko et al.
Revised:  CP'11] , respectively, the classification of {0,1}-valued languages containing all unary functions 
Edit intent: clarity
Original:  [JACM'06] , the classifications of finite-valued languages on two-element and three-element domains obtained by Cohen et al.
Revised:  [JACM'06] ; the classifications of finite-valued languages on two-element and three-element domains obtained by Cohen et al.
Edit intent: fluency
Original:  [AIJ'06 and Huber et al.
Revised:  [AIJ'06 ,
Edit intent: coherence
Original:  SODA'13] , respectively, and the classification of finite-valued languages containing all {0,1}-valued unary functions obtained by Kolmogorov and Zivny [SODA'12   ].
Revised:  SODA'13] ; the classification of finite-valued languages containing all {0,1}-valued unary functions obtained by Kolmogorov and Zivny [SODA'12 ].
Edit intent: coherence
Original:  SODA'13] , respectively, and the classification of finite-valued languages containing all {0,1}-valued unary functions obtained by Kolmogorov and Zivny [SODA'12   ].
Revised:  SODA'13] , respectively, and the classification of finite-valued languages containing all {0,1}-valued unary functions [SODA'12 ].
Edit intent: coherence
Original:  We show that every core language Gamma either admits a binary idempotent and symmetric fractional polymorphism in which case the basic linear programming relaxation solves any instance of VCSP(Gamma ) exactly, or Gamma satisfies a simple hardness condition that allows for a polynomial-time reduction from Max-Cut to VCSP(Gamma).
Revised:  We show that every core language Gamma either admits a binary symmetric fractional polymorphism in which case the basic linear programming relaxation solves any instance of VCSP(Gamma ) exactly, or Gamma satisfies a simple hardness condition that allows for a polynomial-time reduction from Max-Cut to VCSP(Gamma).
Edit intent: clarity
Original:  The proof uses a variation of Motzkin's Transposition Theorem, hyperplane arrangements, and a technique recently introduced by Kolmogorov arXiv:1207.7213%DIFDELCMD < ] %%% reformulated using Markov chains.
Revised:  The proof uses a variation of Motzkin's Transposition Theorem, hyperplane arrangements, and a technique recently introduced by Kolmogorov %DIFDELCMD < ] %%% reformulated using Markov chains.
Edit intent: coherence
Original:  the classification of finite-valued languages containing all 0,1%DIFDELCMD < }%%% -valued unary functions SODA'12%DIFDELCMD < ]%%% ;
Revised:  the classification of finite-valued languages containing all 0,1%DIFDELCMD < }%%% SODA'12%DIFDELCMD < ]%%% ;
Edit intent: clarity
Original:  the classification of finite-valued languages containing all 0,1%DIFDELCMD < }%%% -valued unary functions SODA'12%DIFDELCMD < ]%%% ;
Revised:  the classification of finite-valued languages containing all 0,1%DIFDELCMD < }%%% -valued unary functions %DIFDELCMD < ]%%% ;
Edit intent: coherence
Original: We study the computational complexity of exact minimisation of separable rational-valued discrete functions.
Revised: We study the computational complexity of exact minimisation of rational-valued discrete functions.
Edit intent: clarity
Original: This paper provide a method to calculate the bar codes of a PCD with real coefficient in Section 3.
Revised: This paper provides a method to calculate the bar codes of a PCD with real coefficient in Section 3.
Edit intent: fluency
Original:  The privileged complexity of the Thue-Morse words is also briefly studied.
Revised:  The privileged complexity of the Thue-Morse word is also briefly studied.
Edit intent: fluency
Original: When modeling co-expression networks from high-throughput time course data, the Pearson correlation function is reasonably effective .
Revised: When modeling coexpression networks from high-throughput time course data, the Pearson correlation function is reasonably effective .
Edit intent: fluency
Original:  However, this approach is limited since it cannot capture non-linear interactions and time shifts between the signals .
Revised:  However, its reliability is limited since it cannot capture non-linear interactions and time shifts between the signals .
Edit intent: clarity
Original:  However, this approach is limited since it cannot capture non-linear interactions and time shifts between the signals .
Revised:  However, this approach is limited since it cannot capture non-linear interactions and time shifts .
Edit intent: clarity
Original:  By using a network comparison metric to quantify differences, we show the effectiveness of the DTWMIC approach on both synthetic and transcriptomic datasets.
Revised:  By using a network comparison metric to quantify network differences, the effectiveness of the DTWMIC approach on both synthetic and transcriptomic datasets.
Edit intent: clarity
Original:  By using a network comparison metric to quantify differences, we show the effectiveness of the DTWMIC approach on both synthetic and transcriptomic datasets.
Revised:  By using a network comparison metric to quantify differences, we show the effectiveness of the DTW-MIC approach is demonstrated on both synthetic and transcriptomic datasets.
Edit intent: clarity
Original:  For the general, nonbinary variant, the only previously-known algorithm provides a (d+1)-approximation for trees with outdegree at most d  . Here we show that nonbinary MAF has a polynomial-time 4-approximation and an (exact) fixed-parameter tractable algorithm that runs in O(4^k poly(n)) time.
Revised:  The general, nonbinary variant, the only previously-known algorithm provides a (d+1)-approximation for trees with outdegree at most d . Here we show that nonbinary MAF has a polynomial-time 4-approximation and an (exact) fixed-parameter tractable algorithm that runs in O(4^k poly(n)) time.
Edit intent: fluency
Original:  For the general, nonbinary variant, the only previously-known algorithm provides a (d+1)-approximation for trees with outdegree at most d  . Here we show that nonbinary MAF has a polynomial-time 4-approximation and an (exact) fixed-parameter tractable algorithm that runs in O(4^k poly(n)) time.
Revised:  For the general, nonbinary problem is known to have a (d+1)-approximation for trees with outdegree at most d . Here we show that nonbinary MAF has a polynomial-time 4-approximation and an (exact) fixed-parameter tractable algorithm that runs in O(4^k poly(n)) time.
Edit intent: clarity
Original:   There has been considerable interest in a special case of this problem, in which the input trees are required to be binary.
Revised:  There has been considerable interest in the special cases of these problems in which the input trees are required to be binary.
Edit intent: fluency
Original:  Here we show that nonbinary MAF has a polynomial-time 4-approximation and an (exact) fixed-parameter tractable algorithm that runs in O(4^k poly(n)) time .
Revised:  Here we show that nonbinary MAF has a polynomial-time 4-approximation and a fixed-parameter tractable (exact) fixed-parameter tractable algorithm that runs in O(4^k poly(n)) time .
Edit intent: clarity
Original:  Here we show that nonbinary MAF has a polynomial-time 4-approximation and an (exact) fixed-parameter tractable algorithm that runs in O(4^k poly(n)) time .
Revised:  Here we show that nonbinary MAF has a polynomial-time 4-approximation and an (exact) algorithm that runs in O(4^k poly(n)) time .
Edit intent: clarity
Original:  The algorithms have been implemented and are publicly available.
Revised:  The algorithms have been implemented and made publicly available.
Edit intent: clarity
Original:  This is a formalisation of a well-known observation that many quantum query algorithms only require  knowledge of the disposition of possible certificates in the input string, not the precise values therein.
Revised:  This is a formalisation of a well-known observation that many quantum query algorithms only require the knowledge of the disposition of possible certificates in the input string, not the precise values therein.
Edit intent: fluency
Original:  Next, we derive a dual formulation of the complexity of a non-adaptive learning graph, and use it to show that non-adaptive learning graphs are tight for certificate structures defined by certificates of bounded size .
Revised:  Next, we derive a dual formulation of the complexity of a non-adaptive learning graph, and use it to show that non-adaptive learning graphs are tight for all certificate structures .
Edit intent: clarity
Original:  By this, we mean that there exists a function possessing the certificate structure  such that a learning graph gives an optimal quantum query algorithm for this function.
Revised:  By this, we mean that there exists a function possessing the certificate structure and such that a learning graph gives an optimal quantum query algorithm for this function.
Edit intent: clarity
Original:  Instead of attempting to rely on infinities such as idealized limits of infinite time or numerical precision, or some other physically unattainable source, the field should be geared toward extending the classical paradigm to better encapsulate modern computational problems that are not well-expressed/modeled by the closed-system paradigm of the Turing machine.
Revised:  Instead of attempting to rely on infinities such as idealized limits of infinite time or numerical precision, or some other physically unattainable source, one should focus on extending the classical paradigm to better encapsulate modern computational problems that are not well-expressed/modeled by the closed-system paradigm of the Turing machine.
Edit intent: clarity
Original:  Statistical methodologies of point estimates such as the LASSO algorithm have been proposed to identify the interactions of miRNA and mRNA based on sequence and expression data.
Revised:  Statistical methodologies for point estimation, such as the LASSO algorithm have been proposed to identify the interactions of miRNA and mRNA based on sequence and expression data.
Edit intent: clarity
Original:  In this paper, we propose Bayesian LASSO and non-negative Bayesian LASSO to analyze the interactions between miRNA and mRNA using the expression data.
Revised:  In this paper, we propose Bayesian LASSO and non-negative Bayesian LASSO to analyze the interactions between miRNA and mRNA using expression data.
Edit intent: fluency
Original:  The proposed Bayesian methods explore the posterior distributions for those parameters required in the model depicting the miRNA-mRNA interactions.
Revised:  The proposed Bayesian methods explore the posterior distributions for those parameters required to model the miRNA-mRNA interactions.
Edit intent: clarity
Original:  The Bayesian approaches are useful for graphing the inferred effects of the miRNAs on the targets by plotting the posterior distributions of those parameters, and while the point estimate algorithm only provides a single estimate for those parameters .
Revised:  Furthermore, Bayesian methods naturally provide statistical significance to select convincing inferred interactions, while point estimate algorithms require a manually chosen threshold, which is less meaningful, to choose the possible interactions .
Edit intent: coherence
Original: We consider the sectoral composition of a country's GDP, i.e the division into agrarian, industrial, and service sectors.
Revised: We consider the sectoral composition of a country's GDP, i.e .\ the partitioning into agrarian, industrial, and service sectors.
Edit intent: clarity
Original: We consider the sectoral composition of a country's GDP, i.e. \ the partitioning into agrarian, industrial, and service sectors.
Revised: We consider the sectoral composition of a country's GDP, i.e. the partitioning into agrarian, industrial, and service sectors.
Edit intent: clarity
Original: Scarcity of frequencies combined with the demand for more bandwidth is likely to increase the need for devices that provide high wireless bandwidth in limited areas while using a wired network to carry data over longer distances.
Revised: Scarcity of frequencies and the demand for more bandwidth is likely to increase the need for devices that provide high wireless bandwidth in limited areas while using a wired network to carry data over longer distances.
Edit intent: clarity
Original:  To utilize the available frequencies more efficiently radios must be able to  find other users of the frequency bands and adapt so that they are not interfered  .
Revised:  To utilize the available frequencies more efficiently . Radios must be able to find other users of the frequency bands and adapt so that they are not interfered .
Edit intent: fluency
Original:  As transmitters hundreds of kilometers away may cause as much interference as a transmitter located next door , this mechanism can not be based on location alone.
Revised:  As transmitters far away may cause as much interference as a transmitter located next door , this mechanism can not be based on location alone.
Edit intent: clarity
Original:  As transmitters hundreds of kilometers away may cause as much interference as a transmitter located next door , this mechanism can not be based on location alone.
Revised:  As transmitters hundreds of kilometers away may cause as much interference as a transmitter located nearby , this mechanism can not be based on location alone.
Edit intent: clarity
Original:  Central databases can be used for this purpose, but with thousands or millions of radio devices to coordinate a centralized system may not always be ideal .
Revised:  Central databases can be used for this purpose, but require expensive infrastructure and planning to scale .
Edit intent: clarity
Original:  In this paper, we propose a decentralized protocol and architecture for discovering interfering radio devices over the Internet.
Revised:  In this paper, we propose a decentralized protocol and architecture for discovering radio devices over the Internet.
Edit intent: clarity
Original:  The protocol has low bandwidth-, memory- and processing requirements, making it suitable for platforms with limited resources .
Revised:  The protocol has low resource requirements, making it suitable for platforms with limited resources .
Edit intent: clarity
Original:  The protocol has low bandwidth-, memory- and processing requirements, making it suitable for platforms with limited resources .
Revised:  The protocol has low bandwidth-, memory- and processing requirements, making it suitable for implementation on limited platforms .
Edit intent: clarity
Original:  We also describe a proof-of-concept resource allocation algorithm and prove that it converges with information gathered by the discovery protocol .
Revised:  The protocol has also been implemented as proof-of-concept resource allocation algorithm and prove that it converges with information gathered by the discovery protocol .
Edit intent: clarity
Original: As a person learns a new skill, distinct synapses, brain regions, and networks are engaged and change over time.
Revised: As a person learns a new skill, distinct synapses, brain regions, and circuits are engaged and change over time.
Edit intent: clarity
Original:  To better understand the dynamic processes that integrate information across a set of regions to enable the emergence of novel behaviour, we measure brain activity during motor sequencing and characterise network properties based on coherent activity between brain regions.
Revised:  In this paper, we develop methods to examine patterns of correlated activity across a large set of brain regions. Our goal is to identify properties that enable robust learning of a motor skill. We measure brain activity during motor sequencing and characterise network properties based on coherent activity between brain regions.
Edit intent: clarity
Original:  To better understand the dynamic processes that integrate information across a set of regions to enable the emergence of novel behaviour, we measure brain activity during motor sequencing and characterise network properties based on coherent activity between brain regions.
Revised:  To better understand the dynamic processes that integrate information across a set of regions to enable the emergence of novel behaviour, we measure brain activity during motor sequencing and characterize network properties based on coherent activity between brain regions.
Edit intent: fluency
Original:  Using recently developed algorithms to detect time-evolving communities of brain regions that control learning , we find that the complex reconfiguration patterns of local communities can be described parsimoniously by the combined presence of a relatively stiff core of primary sensorimotor and visual regions whose connectivity changes little in time and a flexible periphery of multimodal association regions whose connectivity changes frequently.
Revised:  Using recently developed algorithms to detect time-evolving communities , we find that the complex reconfiguration patterns of local communities can be described parsimoniously by the combined presence of a relatively stiff core of primary sensorimotor and visual regions whose connectivity changes little in time and a flexible periphery of multimodal association regions whose connectivity changes frequently.
Edit intent: clarity
Original:  Using recently developed algorithms to detect time-evolving communities of brain regions that control learning , we find that the complex reconfiguration patterns of local communities can be described parsimoniously by the combined presence of a relatively stiff core of primary sensorimotor and visual regions whose connectivity changes little in time and a flexible periphery of multimodal association regions whose connectivity changes frequently.
Revised:  Using recently developed algorithms to detect time-evolving communities of brain regions that control learning , we find that the complex reconfiguration patterns of the brain's putative functional modules that control learning can be described parsimoniously by the combined presence of a relatively stiff core of primary sensorimotor and visual regions whose connectivity changes little in time and a flexible periphery of multimodal association regions whose connectivity changes frequently.
Edit intent: clarity
Original:  Using recently developed algorithms to detect time-evolving communities of brain regions that control learning , we find that the complex reconfiguration patterns of local communities can be described parsimoniously by the combined presence of a relatively stiff core of primary sensorimotor and visual regions whose connectivity changes little in time and a flexible periphery of multimodal association regions whose connectivity changes frequently.
Revised:  Using recently developed algorithms to detect time-evolving communities of brain regions that control learning , we find that the complex reconfiguration patterns of local communities can be described parsimoniously by the combined presence of a relatively stiff core of primary sensorimotor and visual regions whose connectivity changes little in time and a flexible temporal periphery that is composed primarily of multimodal association regions whose connectivity changes frequently.
Edit intent: clarity