wanyu/IteraTeR_v2 huggingface dataset:
Original: We propose a computational process to measure and simultaneously visualize the interrelationships among any number of DNA sequences which allows , for example, the examination of hundreds or thousands of complete mtDNA genomes.
Revised: We propose a computational method to measure and simultaneously visualize the interrelationships among any number of DNA sequences which allows , for example, the examination of hundreds or thousands of complete mtDNA genomes.
Edit intent: clarity
Original: We propose a computational process to measure and simultaneously visualize the interrelationships among any number of DNA sequences which allows , for example, the examination of hundreds or thousands of complete mtDNA genomes.
Revised: We propose a computational process to measure and visualize interrelationships among any number of DNA sequences which allows , for example, the examination of hundreds or thousands of complete mtDNA genomes.
Edit intent: clarity
Original: We propose a computational process to measure and simultaneously visualize the interrelationships among any number of DNA sequences which allows , for example, the examination of hundreds or thousands of complete mtDNA genomes.
Revised: We propose a computational process to measure and simultaneously visualize the interrelationships among any number of DNA sequences allowing , for example, the examination of hundreds or thousands of complete mtDNA genomes.
Edit intent: coherence
Original:  The process starts by computing an image distancebetween graphical representations of DNA sequences ' composition and proceeds to visualize the inferred interrelationships as a Molecular Distance Map: Each point on the map represents a DNA sequence, and the spatial distance between any two points reflects the degree of structural similarity between the corresponding sequences.
Revised:  The process starts by computing an image distancebetween graphical representations of DNA sequences , and the distances are visualized as a Molecular Distance Map: Each point on the map represents a DNA sequence, and the spatial distance between any two points reflects the degree of structural similarity between the corresponding sequences.
Edit intent: clarity
Original:  The process starts by computing an image distancebetween graphical representations of DNA sequences ' composition and proceeds to visualize the inferred interrelationships as a Molecular Distance Map: Each point on the map represents a DNA sequence, and the spatial distance between any two points reflects the degree of structural similarity between the corresponding sequences.
Revised:  The process starts by computing an image distancebetween graphical representations of DNA sequences ' composition and proceeds to visualize the inferred interrelationships as a Molecular Distance Map: Each point on the map represents a DNA sequence, and the spatial proximity between any two points reflects the degree of structural similarity between the corresponding sequences.
Edit intent: clarity
Original:  This is a general-purpose method that does not require DNA sequence homology and can thus be used to compare similar or vastly different DNA sequences, genomic or computer-generated, of the same length or of different lengths.
Edit intent: coherence
Original:  The graphical representation of DNA sequences utilized in this process is the Chaos Game Representation (CGR) of DNA sequences, which has been shown to be genome- and species-specific and can thus act as a genomic signature.
Revised:  The graphical representation of DNA sequences utilized , Chaos Game Representation (CGR) of DNA sequences, which has been shown to be genome- and species-specific and can thus act as a genomic signature.
Edit intent: coherence
Original:  The graphical representation of DNA sequences utilized in this process is the Chaos Game Representation (CGR) of DNA sequences, which has been shown to be genome- and species-specific and can thus act as a genomic signature.
Revised:  The graphical representation of DNA sequences utilized in this process is the Chaos Game Representation (CGR) , is genome- and species-specific and can thus act as a genomic signature.
Edit intent: coherence
Original:  Consequently, Molecular Distance Maps could inform taxonomic clarifications, species identification, placement of species in existing taxonomic categories, as well as studies of evolutionary history.
Revised:  Consequently, Molecular Distance Maps could inform species identification, placement of species in existing taxonomic categories, as well as studies of evolutionary history.
Edit intent: clarity
Original:  Consequently, Molecular Distance Maps could inform taxonomic clarifications, species identification, placement of species in existing taxonomic categories, as well as studies of evolutionary history.
Revised:  Consequently, Molecular Distance Maps could inform taxonomic clarifications, species identification, taxonomic classifications and, to a certain extent, evolutionary history.
Edit intent: clarity
Original:  The image distance employed in this process, the Structural Dissimilarity Index (DSSIM), implicitly compares the occurrences of oligomers of length up to a given k (herein k=9) in the given DNA sequences.
Revised:  The image distance employed , Structural Dissimilarity Index (DSSIM), implicitly compares the occurrences of oligomers of length up to a given k (herein k=9) in the given DNA sequences.
Edit intent: clarity
Original:  The image distance employed in this process, the Structural Dissimilarity Index (DSSIM), implicitly compares the occurrences of oligomers of length up to a given k (herein k=9) in the given DNA sequences.
Revised:  The image distance employed in this process, the Structural Dissimilarity Index (DSSIM), implicitly compares the occurrences of oligomers of length up to k (herein k=9) in the given DNA sequences.
Edit intent: clarity
Original:  The image distance employed in this process, the Structural Dissimilarity Index (DSSIM), implicitly compares the occurrences of oligomers of length up to a given k (herein k=9) in the given DNA sequences.
Revised:  The image distance employed in this process, the Structural Dissimilarity Index (DSSIM), implicitly compares the occurrences of oligomers of length up to a given k (herein k=9) in DNA sequences.
Edit intent: fluency
Original:  We computed such distances for more than 5 million pairs of complete mitochondrial sequences , and used Multi-Dimensional Scaling (MDS) to obtain Molecular Distance Maps that visually display the sequence relatedness in various taxonomic subsetsof interest : phylum Vertebrata, (super)kingdom Protista, classes Amphibia-Insecta-Mammalia, class Amphibia only , and order Primates  .
Revised:  We computed such distances for more than 5 million pairs of complete mitochondrial genomes , and used Multi-Dimensional Scaling (MDS) to obtain Molecular Distance Maps that visually display the sequence relatedness in various taxonomic subsetsof interest : phylum Vertebrata, (super)kingdom Protista, classes Amphibia-Insecta-Mammalia, class Amphibia only , and order Primates .
Edit intent: clarity
Original:  We computed such distances for more than 5 million pairs of complete mitochondrial sequences , and used Multi-Dimensional Scaling (MDS) to obtain Molecular Distance Maps that visually display the sequence relatedness in various taxonomic subsetsof interest : phylum Vertebrata, (super)kingdom Protista, classes Amphibia-Insecta-Mammalia, class Amphibia only , and order Primates  .
Revised:  We computed such distances for more than 5 million pairs of complete mitochondrial sequences , and used Multi-Dimensional Scaling (MDS) to obtain Molecular Distance Maps that visually display the sequence relatedness in various taxonomic subsetsof interest : phylum Vertebrata, (super)kingdom Protista, classes Amphibia-Insecta-Mammalia, class Amphibia , and order Primates .
Edit intent: coherence
Original:  We provide the optimal control as the solution of a Skorohod reflection problem at a suitable free-boundary surface.
Revised:  We provide the optimal control as the solution of a Skorohod reflection problem at a suitable boundary surface.
Edit intent: clarity
Original:  When the driving semimartingale is specified as an affine process, we obtain a flexible Markovian structure which allows for tractable valuation formulas for most interest rate derivatives .
Revised:  When the driving semimartingale is specified as an affine process, we obtain a flexible Markovian structure .
Edit intent: clarity
Original:  In ecology,  the development of  the L\'evy and area-restricted search (ARS) strategies are emerging as important areas of research .
Revised:  In ecology, the development of the L\'evy and area-restricted search behaviour .
Edit intent: clarity
Original:  Although the processes underlying these strategies differ, they can produce similar movement patterns.
Revised:  Although the processes underlying these models differ, they can produce similar movement patterns.
Edit intent: clarity
Original:  Current methods cannot reliably differentiate between them, partly because the models used to describe these strategies are not directly comparable . 2. Here, we present a method that differentiates between the two strategies .
Revised:  Current methods cannot reliably differentiate between these two models . 2. Here, we present a method that differentiates between the two strategies .
Edit intent: clarity
Original:  Current methods cannot reliably differentiate between them, partly because the models used to describe these strategies are not directly comparable . 2. Here, we present a method that differentiates between the two strategies .
Revised:  Current methods cannot reliably differentiate between them, partly because the models used to describe these strategies are not directly comparable . 2. Here, we present a method that differentiates between the two models .
Edit intent: coherence
Original:  It consists of likelihood functions, including a hidden Markov model, and associated statistical measures that assess the support for each strategy . 3. Using a simulation study, we show that our method can differentiate between the two search strategies over a range of parameter values.
Revised:  It consists of likelihood functions, including a hidden Markov model, and associated statistical measures that assess the support for each strategy . 3. Using a simulation study, we show that our method can differentiate between the two search models over a range of parameter values.
Edit intent: fluency
Original:  It consists of likelihood functions, including  a hidden Markov model, and associated statistical measures that assess the relative support for and absolute fit of each model.
Revised:  It consists of likelihood functions, including one for a hidden Markov model, and associated statistical measures that assess the relative support for and absolute fit of each model.
Edit intent: clarity
Original:  In particular, every graph with maximum degree \Delta has an acyclic chromatic number at most 3{2}\Delta^{4{3}} + O(\Delta) , and a non-repetitive chromatic number at most \Delta^2 + 1.89 \Delta^{5{3} + O(\Delta^{4{3}})} . Also every planar graph with maximum degree \Delta has a facial Thue chromatic number at most \Delta + O(\Delta^\frac 12) and facial Thue chromatic index at most 10.
Revised:  In particular, every graph with maximum degree \Delta has an acyclic chromatic number at most 3{2}\Delta^{4{3}} + O(\Delta) , and a non-repetitive chromatic number at most \Delta^2 + 1.89 \Delta^{5{3} + O(\Delta^{4{3}})} . Also every planar graph with maximum degree \Delta has a facial Thue choice number at most \Delta + O(\Delta^\frac 12) and facial Thue chromatic index at most 10.
Edit intent: fluency
Original:  In particular, every graph with maximum degree \Delta has an acyclic chromatic number at most 3{2}\Delta^{4{3}} + O(\Delta) , and a non-repetitive chromatic number at most \Delta^2 + 1.89 \Delta^{5{3} + O(\Delta^{4{3}})} . Also every planar graph with maximum degree \Delta has a facial Thue chromatic number at most \Delta + O(\Delta^\frac 12) and facial Thue chromatic index at most 10.
Revised:  In particular, every graph with maximum degree \Delta has an acyclic chromatic number at most 3{2}\Delta^{4{3}} + O(\Delta) , and a non-repetitive chromatic number at most \Delta^2 + 1.89 \Delta^{5{3} + O(\Delta^{4{3}})} . Also every planar graph with maximum degree \Delta has a facial Thue chromatic number at most \Delta + O(\Delta^\frac 12) and facial Thue choice index at most 10.
Edit intent: fluency
Original: This paper reports experimental results concerning self-organizing networks of small flying robots without any central infrastructure .
Revised: This paper reports experimental results on self-organizing networks of small flying robots without any central infrastructure .
Edit intent: clarity
Original: This paper reports experimental results concerning self-organizing networks of small flying robots without any central infrastructure .
Revised: This paper reports experimental results concerning self-organizing wireless networks carried by small flying robots without any central infrastructure .
Edit intent: clarity
Original: This paper reports experimental results concerning self-organizing networks of small flying robots without any central infrastructure .
Revised: This paper reports experimental results concerning self-organizing networks of small flying robots .
Edit intent: clarity
Original:  The communication between UAVs is a crucial and very challenging aspect.
Revised:  Due to the high mobility of the nodes, maintaining a communication link between the UAVs is a crucial and very challenging aspect.
Edit intent: clarity
Original:  From the analysis of the SAT structure using the elements, we show that the coefficients of the normal vector of the facet can be expressed with the natural number system of which the exponent is exponential in the input size.
Revised:  From the analysis of the SAT problem using the elements, we show that the coefficients of the normal vector of the facet can be expressed with the natural number system of which the exponent is exponential in the input size.
Edit intent: clarity
Original:  Furthermore, we prove that an integral point, which is not contained in the solution region, can locate exponentially near the projected polytope by the number system .
Revised:  This exponential property is caused by the number system .
Edit intent: coherence
Original:  Finally, we show that the number system is not formed in 2-SAT, but partially formed in Horn-SAT  according to the feasible value of a dominant variable, and always formed in k-SAT (k>2) regardless of the feasible value of a dominant variable.
Revised:  Finally, we show that the number system and Horn-SAT according to the feasible value of a dominant variable, and always formed in k-SAT (k>2) regardless of the feasible value of a dominant variable.
Edit intent: clarity
Original:  The sampler is available as an open-source BEAST2 package URL ancestors/).
Revised:  The sampler is available as an open-source BEAST2 package URL 
Edit intent: coherence
Original: A commonly studied means of parameterizing graph problems is the deletion distance from triviality (Guo et al. 2004), which measures the number of vertices that need to be deleted from a graph to place it in some class for which efficient algorithms are known.
Revised: A commonly studied means of parameterizing graph problems is the deletion distance from triviality (Guo et al. 2004), which counts vertices that need to be deleted from a graph to place it in some class for which efficient algorithms are known.
Edit intent: clarity
Original:  We establish that graph isomorphism is FPT when parameterized by elimination distance to bounded degree, generalising results of Bouland et al. (2012) on isomorphism parameterized by tree-depth .
Revised:  We establish that graph isomorphism is FPT when parameterized by elimination distance to bounded degree, extending results of Bouland et al. (2012) on isomorphism parameterized by tree-depth .
Edit intent: clarity
Original:  We establish that graph isomorphism is FPT when parameterized by elimination distance to bounded degree, generalising results of Bouland et al. (2012) on isomorphism parameterized by tree-depth .
Revised:  We establish that graph isomorphism is FPT when parameterized by elimination distance to bounded degree, generalising results of Bouland et al. (2012) .
Edit intent: coherence
Original: Sparse signal approximation can be formulated as the mixed \ell_2-\ell_0 minimization problem \min_x J(x;\lambda)= \|y-Ax  \|  _2^2+\lambda\|x\| _0. We propose two heuristic search algorithms to minimize J for a continuum of \lambda -values, yielding a sequence of coarse to fine approximations . Continuation Single Best Replacement is a bidirectional greedy algorithm adapted from the Single Best Replacement algorithm  previously proposed for minimizing J for fixed \lambda.
Revised: Sparse signal restoration is usually formulated as the mixed \ell_2-\ell_0 minimization problem \min_x J(x;\lambda)= \|y-Ax \| _2^2+\lambda\|x\| _0. We propose two heuristic search algorithms to minimize J for a continuum of \lambda -values, yielding a sequence of coarse to fine approximations . Continuation Single Best Replacement is a bidirectional greedy algorithm adapted from the Single Best Replacement algorithm previously proposed for minimizing J for fixed \lambda.
Edit intent: clarity
Original: Sparse signal approximation can be formulated as the mixed \ell_2-\ell_0 minimization problem \min_x J(x;\lambda)= \|y-Ax  \|  _2^2+\lambda\|x\| _0. We propose two heuristic search algorithms to minimize J for a continuum of \lambda -values, yielding a sequence of coarse to fine approximations . Continuation Single Best Replacement is a bidirectional greedy algorithm adapted from the Single Best Replacement algorithm  previously proposed for minimizing J for fixed \lambda.
Revised: Sparse signal approximation can be formulated as the minimization of a quadratic cost function \|y-Ax \| _2^2+\lambda\|x\| _0. We propose two heuristic search algorithms to minimize J for a continuum of \lambda -values, yielding a sequence of coarse to fine approximations . Continuation Single Best Replacement is a bidirectional greedy algorithm adapted from the Single Best Replacement algorithm previously proposed for minimizing J for fixed \lambda.
Edit intent: clarity
Original: Sparse signal approximation can be formulated as the mixed \ell_2-\ell_0 minimization problem \min_x J(x;\lambda)= \|y-Ax  \|  _2^2+\lambda\|x\| _0. We propose two heuristic search algorithms to minimize J for a continuum of \lambda -values, yielding a sequence of coarse to fine approximations . Continuation Single Best Replacement is a bidirectional greedy algorithm adapted from the Single Best Replacement algorithm  previously proposed for minimizing J for fixed \lambda.
Revised: Sparse signal approximation can be formulated as the mixed \ell_2-\ell_0 minimization problem \min_x J(x;\lambda)= \|y-Ax \| y-Ax\| _2^2+\lambda\|x\| _0. We propose two heuristic search algorithms to minimize J for a continuum of \lambda -values, yielding a sequence of coarse to fine approximations . Continuation Single Best Replacement is a bidirectional greedy algorithm adapted from the Single Best Replacement algorithm previously proposed for minimizing J for fixed \lambda.
Edit intent: fluency
Original: Sparse signal approximation can be formulated as the mixed \ell_2-\ell_0 minimization problem \min_x J(x;\lambda)= \|y-Ax  \|  _2^2+\lambda\|x\| _0. We propose two heuristic search algorithms to minimize J for a continuum of \lambda -values, yielding a sequence of coarse to fine approximations . Continuation Single Best Replacement is a bidirectional greedy algorithm adapted from the Single Best Replacement algorithm  previously proposed for minimizing J for fixed \lambda.
Revised: Sparse signal approximation can be formulated as the mixed \ell_2-\ell_0 minimization problem \min_x J(x;\lambda)= \|y-Ax \| _2^2+\lambda\|x\| _1 with respect to x for a continuum of \lambda -values, yielding a sequence of coarse to fine approximations . Continuation Single Best Replacement is a bidirectional greedy algorithm adapted from the Single Best Replacement algorithm previously proposed for minimizing J for fixed \lambda.
Edit intent: clarity
Original: Sparse signal approximation can be formulated as the mixed \ell_2-\ell_0 minimization problem \min_x J(x;\lambda)= \|y-Ax  \|  _2^2+\lambda\|x\| _0. We propose two heuristic search algorithms to minimize J for a continuum of \lambda -values, yielding a sequence of coarse to fine approximations . Continuation Single Best Replacement is a bidirectional greedy algorithm adapted from the Single Best Replacement algorithm  previously proposed for minimizing J for fixed \lambda.
Revised: Sparse signal approximation can be formulated as the mixed \ell_2-\ell_0 minimization problem \min_x J(x;\lambda)= \|y-Ax \| _2^2+\lambda\|x\| _0. We propose two heuristic search algorithms to minimize J for a continuum of \lambda -values, yielding a sequence of coarse to fine approximations . Continuation Single Best Replacement is a forward-backward greedy strategy extending the Single Best Replacement algorithm previously proposed for minimizing J for fixed \lambda.
Edit intent: clarity
Original: Sparse signal approximation can be formulated as the mixed \ell_2-\ell_0 minimization problem \min_x J(x;\lambda)= \|y-Ax  \|  _2^2+\lambda\|x\| _0. We propose two heuristic search algorithms to minimize J for a continuum of \lambda -values, yielding a sequence of coarse to fine approximations . Continuation Single Best Replacement is a bidirectional greedy algorithm adapted from the Single Best Replacement algorithm  previously proposed for minimizing J for fixed \lambda.
Revised: Sparse signal approximation can be formulated as the mixed \ell_2-\ell_0 minimization problem \min_x J(x;\lambda)= \|y-Ax \| _2^2+\lambda\|x\| _0. We propose two heuristic search algorithms to minimize J for a continuum of \lambda -values, yielding a sequence of coarse to fine approximations . Continuation Single Best Replacement is a bidirectional greedy algorithm adapted from the Single Best Replacement algorithm , previously proposed for minimizing J for fixed \lambda.
Edit intent: fluency
Original:  Numerous methods based on the coalescent process have been proposed for estimation of the phylogenetic species tree given multi-locus DNA sequence data.
Revised:  Numerous methods based on the coalescent process have been proposed for estimation of the phylogenetic species tree given DNA sequence data.
Edit intent: clarity
Original:  We prove that the unrooted topology of the n-leaf phylogenetic species tree is generically identifiable given observed data at the leaves of the tree that are assumed to have arisen from the coalescent process with time-reversible substitution  .
Revised:  We prove that the unrooted topology of the n-leaf phylogenetic species tree is generically identifiable given observed data at the leaves of the tree that are assumed to have arisen from the coalescent process under a time-reversible substitution .
Edit intent: clarity
Original: The time variation of contacts in a networked system may fundamentally alter the properties of spreading processes occurring on it and affect the condition at which epidemics become possible ,
Revised: The time variation of contacts in a networked system may fundamentally alter the properties of spreading processes and affect the condition at which epidemics become possible ,
Edit intent: clarity
Original: The time variation of contacts in a networked system may fundamentally alter the properties of spreading processes occurring on it and affect the condition at which epidemics become possible ,
Revised: The time variation of contacts in a networked system may fundamentally alter the properties of spreading processes occurring on it and affect the condition for large-scale propagation ,
Edit intent: clarity