wanyu/IteraTeR_v2 huggingface dataset:
Original:  When block-separable constraints are also present, randomized FW has been shown to further reduce complexity by updating only a fraction of coordinate blocks per iteration.
Revised:  When block-separable constraints are also present, randomized block FW (RB-FW) has been shown to further reduce complexity by updating only a fraction of coordinate blocks per iteration.
Edit intent: clarity
Original:  In this context , the present work develops feasibility-ensuring step sizes , and provably convergent randomized block Frank-Wolfe ( RB-FW ) solvers that are flexible in selecting the number of blocks to update per iteration . Convergence rates of RB-FW are established through computational bounds on a primal sub-optimality measure , and on the duality gap.
Revised:  To circumvent the limitations of existing methods , the present work develops feasibility-ensuring step sizes , and provably convergent randomized block Frank-Wolfe ( RB-FW ) solvers that are flexible in selecting the number of blocks to update per iteration . Convergence rates of RB-FW are established through computational bounds on a primal sub-optimality measure , and on the duality gap.
Edit intent: clarity
Original:  In this context , the present work develops feasibility-ensuring step sizes , and provably convergent randomized block Frank-Wolfe ( RB-FW ) solvers that are flexible in selecting the number of blocks to update per iteration . Convergence rates of RB-FW are established through computational bounds on a primal sub-optimality measure , and on the duality gap.
Revised:  In this context , the present work develops step sizes for RB-FW ) solvers that are flexible in selecting the number of blocks to update per iteration . Convergence rates of RB-FW are established through computational bounds on a primal sub-optimality measure , and on the duality gap.
Edit intent: clarity
Original:  In this context , the present work develops feasibility-ensuring step sizes , and provably convergent randomized block Frank-Wolfe ( RB-FW ) solvers that are flexible in selecting the number of blocks to update per iteration . Convergence rates of RB-FW are established through computational bounds on a primal sub-optimality measure , and on the duality gap.
Revised:  In this context , the present work develops feasibility-ensuring step sizes , and provably convergent randomized block Frank-Wolfe ( RB-FW that enable a flexible selection of the number of blocks to update per iteration . Convergence rates of RB-FW are established through computational bounds on a primal sub-optimality measure , and on the duality gap.
Edit intent: clarity
Original:  In this context , the present work develops feasibility-ensuring step sizes , and provably convergent randomized block Frank-Wolfe ( RB-FW ) solvers that are flexible in selecting the number of blocks to update per iteration . Convergence rates of RB-FW are established through computational bounds on a primal sub-optimality measure , and on the duality gap.
Revised:  In this context , the present work develops feasibility-ensuring step sizes , and provably convergent randomized block Frank-Wolfe ( RB-FW ) solvers that are flexible in selecting the number of blocks to update per iteration . Convergence rates of RB-FW are established through computational bounds on a primal sub-optimality measure and on the duality gap.
Edit intent: fluency
Original:  Different from existing convergence analysis, which only applies to a step-size sequence that does not generally lead to feasible iterates , the analysis here includes two classes of step-size sequences that not only guarantee feasibility of the iterates , but also enhance flexibility in choosing decay rates.
Revised:  Different from existing convergence analysis, which only applies to a step-size sequence that does not generally lead to feasible iterates . Furthermore, two classes of step-size sequences that not only guarantee feasibility of the iterates , but also enhance flexibility in choosing decay rates.
Edit intent: coherence
Original:  Different from existing convergence analysis, which only applies to a step-size sequence that does not generally lead to feasible iterates , the analysis here includes two classes of step-size sequences that not only guarantee feasibility of the iterates , but also enhance flexibility in choosing decay rates.
Revised:  Different from existing convergence analysis, which only applies to a step-size sequence that does not generally lead to feasible iterates , the analysis here includes two classes of step-size sequences that guarantee feasibility of the iterates , but also enhance flexibility in choosing decay rates.
Edit intent: fluency
Original:  Different from existing convergence analysis, which only applies to a step-size sequence that does not generally lead to feasible iterates , the analysis here includes two classes of step-size sequences that not only guarantee feasibility of the iterates , but also enhance flexibility in choosing decay rates.
Revised:  Different from existing convergence analysis, which only applies to a step-size sequence that does not generally lead to feasible iterates , the analysis here includes two classes of step-size sequences that not only guarantee feasibility of the iterates are also proposed to enhance flexibility in choosing decay rates.
Edit intent: clarity
Original:  Simulated tests demonstrate the impressive performance improvement of RB-FW relative to existing randomized single-block FW methods.
Revised:  Simulated tests demonstrate the performance improvement of RB-FW relative to existing randomized single-block FW methods.
Edit intent: clarity
Original: Usually, given a continuous-time nonlinear model, a closed form solution for an exact discretization can not be found explicitly, originating the need of approximating discrete-time models.
Revised: Usually, given a continuous-time nonlinear model, a closed form solution for an exact discretization cannot be found explicitly, originating the need of approximating discrete-time models.
Edit intent: fluency
Original: In this paper, we propose a mapping of spreading dynamics to  weighted networks, where weights represent interaction time delayson edges.
Revised: We propose a mapping of spreading dynamics to weighted networks, where weights represent interaction time delayson edges.
Edit intent: clarity
Original: In this paper, we propose a mapping of spreading dynamics to  weighted networks, where weights represent interaction time delayson edges.
Revised: In this paper, we propose a mapping of spreading dynamics to an ensemble of weighted networks, where weights represent interaction time delayson edges.
Edit intent: clarity
Original:   Our framework provides insights into the local and global spreading dynamics , enables efficient source detection , and helps to improve strategies for time-critical vaccination.
Revised:  Our framework provides insights into the local and global spreading dynamics , enables efficient source detection and helps to improve strategies for time-critical vaccination.
Edit intent: fluency
Original:  Finally, we establish the connection of our mapping to bond percolationtheory .
Revised:  Finally, we establish the connection of our mapping with bond percolation .
Edit intent: clarity
Original:  Furthermore, it enables efficient source detection and helps to improve strategies for time-critical vaccination .
Revised:  Furthermore, we have employed our framework to perform efficient source detection and helps to improve strategies for time-critical vaccination .
Edit intent: clarity
Original:  Furthermore, it enables efficient source detection and helps to improve strategies for time-critical vaccination .
Revised:  Furthermore, it enables efficient source detection and to improve strategies for time-critical vaccination .
Edit intent: clarity
Original:  We briefly discuss the research questions that can be investigated with this dataset.
Revised:  We briefly discuss the research questions that can be supported by this dataset.
Edit intent: clarity
Original: We introduce a dataset for facilitating audio-visual analysis of musical performances.
Revised: We introduce a dataset for facilitating audio-visual analysis of music performances.
Edit intent: fluency
Original:  The dataset comprises a number of simple multi-instrument classical music pieces assembled from coordinated but separately recorded performances of individual tracks.
Revised:  The dataset comprises 44 simple multi-instrument classical music pieces assembled from coordinated but separately recorded performances of individual tracks.
Edit intent: clarity
Original:  We describe our methodology for the creation of this dataset, particularly highlighting our approaches for addressing the challenges involved in maintaining synchronization and naturalness.
Revised:  We describe our methodology for the creation of the dataset, particularly highlighting our approaches for addressing the challenges involved in maintaining synchronization and naturalness.
Edit intent: fluency
Original:  We compare this dataset with existing widely used music audio datasets on the synchronization quality and show its high quality .
Revised:  We compare this dataset with existing widely-used music audio datasets on the synchronization quality and show its high quality .
Edit intent: fluency
Original:  We compare this dataset with existing widely used music audio datasets on the synchronization quality and show its high quality .
Revised:  We compare this dataset with existing widely used music audio datasets .
Edit intent: coherence
Original:  We anticipate that the dataset will be useful for the development and evaluation of many existing music information retrieval (MIR) tasks, as well as many novel multi-modal tasks.
Revised:  We anticipate that the dataset will be useful for the development and evaluation of existing music information retrieval (MIR) tasks, as well as many novel multi-modal tasks.
Edit intent: fluency
Original:  We anticipate that the dataset will be useful for the development and evaluation of many existing music information retrieval (MIR) tasks, as well as many novel multi-modal tasks.
Revised:  We anticipate that the dataset will be useful for the development and evaluation of many existing music information retrieval (MIR) tasks, as well as for novel multi-modal tasks.
Edit intent: clarity
Original:  On this end, we benchmark this dataset with existing music audio datasets using two existing MIR tasks (multi-pitch analysis and score-informed source separation) .
Revised:  We benchmark two existing MIR tasks (multi-pitch analysis and score-informed source separation) .
Edit intent: clarity
Original:  Finally, we propose several emerging research directions that can be supported by this dataset .
Revised:  Finally, we propose several emerging research directions that the dataset enables .
Edit intent: clarity
Original:  Here we compute the probability that a pair of randomly chosen mutations interacts sign-epistatically, which is found to decrease algebraically with increasing phenotypic dimension n, and varies non-monotonically with the distance from the phenotypic optimum.
Revised:  Here we compute the probability that a pair of randomly chosen mutations interacts sign-epistatically, which is found to decrease with increasing phenotypic dimension n, and varies non-monotonically with the distance from the phenotypic optimum.
Edit intent: clarity
Original:  We then derive asymptotic expressions for the mean number of fitness maxima in genotypic landscapes composed of all combinations of L random mutations.
Revised:  We then derive expressions for the mean number of fitness maxima in genotypic landscapes composed of all combinations of L random mutations.
Edit intent: clarity
Original:  This number increases exponentially with L, and the corresponding growth rate is used as a measure of the complexity of the genotypic landscape.
Revised:  This number increases exponentially with L, and the corresponding growth rate is used as a measure of the complexity of the landscape.
Edit intent: clarity
Original:  The dependence of the complexity on the parameters of the model is found to be surprisingly rich, and three distinct phases characterized by different landscape structures are identified.
Revised:  The dependence of the complexity on the model parameters is found to be surprisingly rich, and three distinct phases characterized by different landscape structures are identified.
Edit intent: clarity
Original:  The complexity generally decreases with increasing phenotypic dimension, but a non-monotonic dependence on n is found in certain regimes .
Revised:  Our analysis shows that the phenotypic dimension, but a non-monotonic dependence on n is found in certain regimes .
Edit intent: clarity
Original:  Our results  inform the interpretation of experiments where the parameters of Fisher's model have been inferred from data, and help to elucidate which features of empirical fitness landscapes can (or cannot) be described by this model.
Revised:  Our results inform the interpretation of experiments where the parameters of Fisher's model have been inferred from data, and help to elucidate which features of empirical fitness landscapes can be described by this model.
Edit intent: clarity
Original:  Here we compute the probability that a pair of randomly chosen mutations interacts sign-epistatically , which is found to decrease with increasing phenotypic dimension n, and varies non-monotonically with the distance from the phenotypic optimum.
Revised:  Here we compute the probability that a pair of randomly chosen mutations interacts sign epistatically , which is found to decrease with increasing phenotypic dimension n, and varies non-monotonically with the distance from the phenotypic optimum.
Edit intent: fluency
Original:  Here we compute the probability that a pair of randomly chosen mutations interacts sign-epistatically , which is found to decrease with increasing phenotypic dimension n, and varies non-monotonically with the distance from the phenotypic optimum.
Revised:  Here we compute the probability that a pair of randomly chosen mutations interacts sign-epistatically , which is found to decrease with increasing phenotypic dimension n, and varies nonmonotonically with the distance from the phenotypic optimum.
Edit intent: fluency
Original:  We then derive expressions for the mean number of fitness maxima in genotypic landscapes composed of all combinations of L random mutations.
Revised:  We then derive expressions for the mean number of fitness maxima in genotypic landscapes comprised of all combinations of L random mutations.
Edit intent: fluency
Original: The Galois /monodromy group of a parameterized polynomial system of equations encodes the structure of the solutions.
Revised: The Galois group of a parameterized polynomial system of equations encodes the structure of the solutions.
Edit intent: clarity
Original:  This  group acts on the  fiber of a projection from the incidence variety of parameters and solutions to the space of parameters.
Revised:  This group acts on the fiber of a projection from the incidence variety of parameters and solutions onto the space of parameters.
Edit intent: fluency
Original:  For connected bipartite graphs, this is equivalent to the condition that every edge is contained in some maximum matching.
Edit intent: coherence
Original:  When the input graph is unbalanced , the problem is solved via matroid intersection.
Revised:  When the input graph is not balanced , the problem is solved via matroid intersection.
Edit intent: clarity
Original:  Both results also lead to similar min-max characterizations of the minimum number, which generalize the result of Eswaran and Tarjan .
Revised:  These results also lead to similar min-max characterizations of the minimum number, which generalize the result of Eswaran and Tarjan .
Edit intent: fluency
Original:  Both results also lead to similar min-max characterizations of the minimum number, which generalize the result of Eswaran and Tarjan .
Revised:  Both results also lead to min-max characterizations of the minimum number, which generalize the result of Eswaran and Tarjan .
Edit intent: clarity
Original:  Applications to data transmission over packet networks based on multipath routing are discussed.
Edit intent: clarity
Original: This paper is motivated by the error-control problem in communication channels in which the transmitted sequences are subjected to random permutations, in addition to being impaired with insertions, deletions, substitutions, and erasures of symbols.
Revised: Motivated by communication channels in which the transmitted sequences are subjected to random permutations, in addition to being impaired with insertions, deletions, substitutions, and erasures of symbols.
Edit intent: clarity
Original: This paper is motivated by the error-control problem in communication channels in which the transmitted sequences are subjected to random permutations, in addition to being impaired with insertions, deletions, substitutions, and erasures of symbols.
Revised: This paper is motivated by the error-control problem in communication channels in which the transmitted sequences are subject to random permutations, in addition to being impaired with insertions, deletions, substitutions, and erasures of symbols.
Edit intent: fluency
Original: Motivated by communication channels in which the transmitted sequences are subject to random permutations, as well as by  DNA storage systems, we study the error control problem in settings where the information is stored/transmitted in the form of multisets of symbols from a given finite alphabet.
Revised: Motivated by communication channels in which the transmitted sequences are subject to random permutations, as well as by certain DNA storage systems, we study the error control problem in settings where the information is stored/transmitted in the form of multisets of symbols from a given finite alphabet.
Edit intent: clarity
Original:  The construction based on the notion of Sidon sets in finite Abelian groups is shown to be optimal, in the sense of minimal asymptotic code redundancy, for any "error radius" and any alphabet size.
Revised:  The construction based on the notion of Sidon sets in finite Abelian groups is shown to be optimal, in the sense of the asymptotic scaling of code redundancy, for any "error radius" and any alphabet size.
Edit intent: clarity
Original:  For 0.1 bpp, the respective corresponding error rates are of 39\%, 38\%, and 41\%, being always better than the ones provided by SRM+EC.
Revised:  For 0.1 bpp, the respective corresponding error rates are of 39\%, 38\%, and 41\%, and are always better than the ones provided by SRM+EC.
Edit intent: clarity
Original: In this paper, an existing hyperelastic membrane model of graphene is adapted to curvilinear coordinates and extended to a rotation-free shell formulation based on isogeometric finite elements.
Revised: An existing hyperelastic membrane model of graphene is adapted to curvilinear coordinates and extended to a rotation-free shell formulation based on isogeometric finite elements.
Edit intent: coherence
Original:  Results are in agreement to analytical solutions and satisfy the FE patch test.
Revised:  The results are in agreement to analytical solutions and satisfy the FE patch test.
Edit intent: fluency
Original:  Finally, the performance of the shell formulation for graphene structures is illustrated by the several numerical examples.
Revised:  The performance of the shell formulation for graphene structures is illustrated by the several numerical examples.
Edit intent: coherence
Original:  Finally, the performance of the shell formulation for graphene structures is illustrated by the several numerical examples.
Revised:  Finally, the performance of the shell formulation for graphene structures is illustrated by several numerical examples.
Edit intent: fluency
Original:  The proposed formulation can be extended to other 2D materials.
Revised:  In principle, the proposed formulation can be extended to other 2D materials.
Edit intent: clarity
Original: In this contribution we analyze the phylogenetic information content from a combinatorial point of view by considering the binary relation on the set of taxa defined by the existence of  single event separating two taxa.
Revised: In this contribution we analyze the phylogenetic information content from a combinatorial point of view by consid-ering the binary relation on the set of taxa defined by the existence of single event separating two taxa.
Edit intent: fluency
Original: In this contribution we analyze the phylogenetic information content from a combinatorial point of view by considering the binary relation on the set of taxa defined by the existence of  single event separating two taxa.
Revised: In this contribution we analyze the phylogenetic information content from a combinatorial point of view by considering the binary relation on the set of taxa defined by the existence of a single event separating two taxa.
Edit intent: fluency
Original:  We show that the graph-representation of this relation must be a tree.
Revised:  We showthat the graph-representation of this relation must be a tree.
Edit intent: fluency
Original:  Moreover, we characterize completely the relationship between the tree of such relations and the underlying phylogenetic tree.
Revised:  Moreover, we characterize completely the relationshipbetween the tree of such relations and the underlying phylogenetic tree.
Edit intent: fluency
Original:  With directed operations such as tandem-duplication-random-loss events in mind we demonstrate how non-symmetric information constrains the position of the root in the partially reconstructed phylogeny.
Revised:  With directed operations such as tandem-duplication-random-loss events in mind we demonstrate how non-symmetric information constrains the position ofthe root in the partially reconstructed phylogeny.
Edit intent: fluency
Original: To this date, all methodologies for detecting plagiarism  have focused on investigating the final digital "outcome", eg. a document or source code.
Revised: All methodologies for detecting plagiarism have focused on investigating the final digital "outcome", eg. a document or source code.
Edit intent: clarity
Original: To this date, all methodologies for detecting plagiarism  have focused on investigating the final digital "outcome", eg. a document or source code.
Revised: To this date, all methodologies for detecting plagiarism have focused on the final digital "outcome", eg. a document or source code.
Edit intent: clarity
Original: To this date, all methodologies for detecting plagiarism  have focused on investigating the final digital "outcome", eg. a document or source code.
Revised: To this date, all methodologies for detecting plagiarism have focused on investigating the final digital "outcome", such as a document or source code.
Edit intent: clarity
Original:  We look at interaction logs of an author with the software used for creation of the work.
Revised:  We look at an author's interaction logs with the software used for creation of the work.
Edit intent: clarity
Original:  We look at interaction logs of an author with the software used for creation of the work.
Revised:  We look at interaction logs of an author with the software used to create the work.
Edit intent: clarity
Original:  Detection relies on comparing histograms of command usages of multiple logs .
Revised:  Detection relies on comparing the histograms of multiple logs' command use .
Edit intent: fluency
Original:  A work is classified as plagiarism , if its log deviates too much from logs of "honestly created" works or if its log is too similar to another log.
Revised:  A work is classified as plagiarism if its log deviates too much from logs of "honestly created" works or if its log is too similar to another log.
Edit intent: fluency