wanyu/IteraTeR_v2 huggingface dataset:
Original: Motivated by the randomized generation of slowly synchronizing automata, we study automata made of permutation letters and a merging letter of rank n- 1 . We present a constructive randomized procedure to generate minimal synchronizing automata of that kind with (potentially) large alphabet size based on recent results on primitive sets of matrices.
Revised: Motivated by the randomized generation of slowly synchronizing automata, we study automata made of permutation letters and a merging letter of rank n- 1 . We present a constructive randomized procedure to generate synchronizing automata of that kind with (potentially) large alphabet size based on recent results on primitive sets of matrices.
Edit intent: clarity
Original:  In this work, we improve these results and introduce the new class of single-pair-seq-shellable drawings.
Revised:  In this work, we improve these results and introduce the new class of semi-pair-shellable drawings.
Edit intent: fluency
Original:  We prove the Harary-Hill Conjecture for this new class using novel results on triple cumulated k-edges.
Revised:  We prove the Harary-Hill Conjecture for this new class using novel results on k-edges.
Edit intent: clarity
Original:  So far, all approaches for proving the Harary-Hill Conjecture for specific classes rely on a globally fixed reference face.
Revised:  So far, approaches for proving the Harary-Hill Conjecture for specific classes rely on a globally fixed reference face.
Edit intent: clarity
Original:  So far, all approaches for proving the Harary-Hill Conjecture for specific classes rely on a globally fixed reference face.
Revised:  So far, all approaches for proving the Harary-Hill Conjecture for specific classes rely on a fixed reference face.
Edit intent: clarity
Original:  Using k-deviations, we gain interesting insights into the essence of k-edges, and we further relax the necessity of a fixed reference face .
Revised:  Using k-deviations, we gain interesting insights into the essence of k-edges, and we further relax the necessity of fixed reference faces .
Edit intent: fluency
Original:  This has allowed us to perform first population dynamics simulations of such a type and to calculate the one- and two-order distribution functions in the spatially inhomogeneous case for the first time using the three-order Kirkwood superposition ansatz.
Revised:  This has allowed us to perform first population dynamics simulations of such a class and to calculate the one- and two-order distribution functions in the spatially inhomogeneous case for the first time using the three-order Kirkwood superposition ansatz.
Edit intent: clarity
Original:  The strong clustering followed by the deep disaggregation in the wavefront of spatial propagation for systems with short-range dispersal or long-range competition are identified .
Revised:  The strong clustering followed by deep disaggregation in the wavefront of spatial propagation for systems with short-range dispersal or long-range competition are identified .
Edit intent: fluency
Original:  The strong clustering followed by the deep disaggregation in the wavefront of spatial propagation for systems with short-range dispersal or long-range competition are identified .
Revised:  The strong clustering followed by the deep disaggregation in the wavefront of spatial propagation for systems with short-range dispersal or long-range competition has been observed .
Edit intent: clarity
Original:  In the opposite regime, the asymmetric long-tail behavior of the inhomogeneous pair correlation function is predicted .
Revised:  In the opposite regime, asymmetric long-tail behavior of the inhomogeneous pair correlation function is predicted .
Edit intent: fluency
Original: We propose a novel method for numerical modeling of inhomogeneous spatial moment dynamics of population systems within a continuous-space model with nonlocal dispersal and competition.
Revised: A novel method is proposed for numerical modeling of inhomogeneous spatial moment dynamics of population systems within a continuous-space model with nonlocal dispersal and competition.
Edit intent: clarity
Original: We propose a novel method for numerical modeling of inhomogeneous spatial moment dynamics of population systems within a continuous-space model with nonlocal dispersal and competition.
Revised: We propose a novel method for numerical modeling of spatially inhomogeneous moment dynamics of population systems within a continuous-space model with nonlocal dispersal and competition.
Edit intent: clarity
Original: We propose a novel method for numerical modeling of inhomogeneous spatial moment dynamics of population systems within a continuous-space model with nonlocal dispersal and competition.
Revised: We propose a novel method for numerical modeling of inhomogeneous spatial moment dynamics of populations with nonlocal dispersal and competition.
Edit intent: clarity
Original:  It is based on analytical decompositions of the time evolution operator for the coupled set of kinetic equations.
Revised:  It is based on an analytically solvable decomposition of the time evolution operator for the coupled set of kinetic equations.
Edit intent: clarity
Original:  It is based on analytical decompositions of the time evolution operator for the coupled set of kinetic equations.
Revised:  It is based on analytical decompositions of the time evolution operator for a coupled set of kinetic equations.
Edit intent: fluency
Original:  It is based on analytical decompositions of the time evolution operator for the coupled set of kinetic equations.
Revised:  It is based on analytical decompositions of the time evolution operator for the coupled set of master equations.
Edit intent: clarity
Original:  Moreover, the novel method has enabled us to find new subtle effects which can take place in population systems . Namely, strong clustering followed by deep disaggregation in the wavefront of spatial propagationfor systems with short-range dispersal or long-range competition has been observed.
Revised:  Moreover, the novel method has enabled us to find new subtle effects , possible in real populations . Namely, strong clustering followed by deep disaggregation in the wavefront of spatial propagationfor systems with short-range dispersal or long-range competition has been observed.
Edit intent: clarity
Original:  These features are explained by an interplay between the dispersal and competition interactions in the presence of reproductive pair correlations at inhomogeneous density distributions .
Revised:  These features are explained by an interplay between the dispersal and competition in the presence of reproductive pair correlations at inhomogeneous density distributions .
Edit intent: clarity
Original:  These features are explained by an interplay between the dispersal and competition interactions in the presence of reproductive pair correlations at inhomogeneous density distributions .
Revised:  These features are explained by an interplay between the dispersal and competition interactions in the presence of reproductive pair correlations and the inhomogeneity of the density of the system .
Edit intent: clarity
Original: A novel method is proposed for numerical modeling of spatially inhomogeneous moment dynamics of populations with nonlocal dispersal and competition  .
Revised: We propose a novel method for numerical modeling of spatially inhomogeneous moment dynamics of populations with nonlocal dispersal and competition .
Edit intent: clarity
Original:  It is based on an analytically solvable decomposition of the time evolution operator for a coupled set of master equations.
Revised:  It is based on analytically solvable decompositions of the time evolution operator for a coupled set of master equations.
Edit intent: fluency
Original:  This  allowed us -- for the first time in the literature -- to perform moment dynamics simulations for spatially inhomogeneous systems beyond the mean-field approach and to calculate the second-order correlation function using the Kirkwood superposition ansatz.
Revised:  This has allowed us -- for the first time in the literature -- to perform moment dynamics simulations for spatially inhomogeneous systems beyond the mean-field approach and to calculate the second-order correlation function using the Kirkwood superposition ansatz.
Edit intent: fluency
Original:  This  allowed us -- for the first time in the literature -- to perform moment dynamics simulations for spatially inhomogeneous systems beyond the mean-field approach and to calculate the second-order correlation function using the Kirkwood superposition ansatz.
Revised:  This allowed us -- for the first time in the literature -- to perform moment dynamics simulations of spatially inhomogeneous systems beyond the mean-field approach and to calculate the second-order correlation function using the Kirkwood superposition ansatz.
Edit intent: fluency
Original:  For populations in which the competition range is much shorter than the dispersalrange , the pair correlation function exhibits a long-tail behavior.
Revised:  For populations in which the competition range is much shorter than that of dispersal , the pair correlation function exhibits a long-tail behavior.
Edit intent: clarity
Original:  All these types of behavior are interpreted as a trade-off between the dispersal and competition in the presence of reproductive pair correlations and the inhomogeneity of the density of the system.
Revised:  All these types of behavior are interpreted as a trade-off between the dispersal and competition in the coexistence of reproductive pair correlations and the inhomogeneity of the density of the system.
Edit intent: clarity
Original:  The temporal scales of the dynamics of the financial variables and the macroeconomic fundamentals are very different, which makes the empirical linkage even more interesting and significant.
Revised:  The temporal scales of the dynamics of the financial variables and the macroeconomic fundamentals are very different, which make the empirical linkage even more interesting and significant.
Edit intent: fluency
Original:  Furthermore, we show that the Economic Complexity Index and the equity markets have a positive relationship among themselves, as is the case between Gross Domestic Product.
Revised:  Furthermore, we show that the Economic Complexity Index and the equity markets have a positive relationship among themselves, as is the case for Gross Domestic Product.
Edit intent: clarity
Original: A variety of potentially disease-spreading contact networkscan be naturally modeled with graphs whose structure is subject to discrete changes over time, i.e. with temporal graphs.
Revised: Spreading processes on graphs are a natural model for a wide variety of real-world phenomena, including information spread over social networks and biological diseases spreading over contact networks. Often, the networks over which these processes spread are dynamic in nature, and can be modeled with temporal graphs.
Edit intent: clarity
Original:  In this paper, motivated by network epidemiology applications in the dynamics of disease spreading on a data-derived network, we study the problem of deleting edges and/or edge availabilities from a given temporal graph in order to reduce its (temporal) connectivity.
Revised:  In this paper, motivated by network epidemiology applications in the dynamics of disease spreading on a data-derived network, we study the problem of deleting edges from a given temporal graph in order to reduce its (temporal) connectivity.
Edit intent: clarity
Original:  In particular, our aim is to find a temporal subgraph , in which the potential disease of any vertex u can be transferred to only a limited number of other vertices v using a temporal path(i. e. a path from u to v, along which the times of the edge availabilities increase).
Revised:  In particular, our aim is to find a temporal subgraph in which a process starting at any single vertex can be transferred to only a limited number of other vertices v using a temporal path(i. e. a path from u to v, along which the times of the edge availabilities increase).
Edit intent: clarity
Original:  We introduce two natural deletion problems for temporal graphs (for deletion of edges and of edge availabilities, respectively) and we provide positive and negative results on their computational complexity , both in the traditional and the parameterized sense, subject to various natural parameters .
Revised:  We introduce two natural deletion problems for temporal graphs and provide positive and negative results on their computational complexity , both in the traditional and the parameterized sense, subject to various natural parameters .
Edit intent: coherence
Original:  We introduce two natural deletion problems for temporal graphs (for deletion of edges and of edge availabilities, respectively) and we provide positive and negative results on their computational complexity , both in the traditional and the parameterized sense, subject to various natural parameters .
Revised:  We introduce two natural deletion problems for temporal graphs (for deletion of edges and of edge availabilities, respectively) and we provide positive and negative results on its computational complexity and approximability .
Edit intent: clarity
Original:  The well-known shortest remaining processing time (SRPT) policy is optimal in the perfect-information scenario, and the more complex Gittins index policy is optimal in the zero-information scenario.
Revised:  The well-known shortest remaining processing time (SRPT) policy is optimal in the perfect-information scenario, and the more complex Gittins policy is optimal in the zero-information scenario.
Edit intent: clarity
Original:  We introduce a new job model, that of multistage jobs, to capture the partial-information scenario.
Revised:  We introduce a new job model, that of multistage jobs, to capture this partial-information scenario.
Edit intent: fluency
Original:  In these languages, the subtyping relation between ground object types ( ones with no type variables ) is the basis for defining the full OO subtyping relation ( i.e., that includes type variables ).
Revised:  In these languages, the subtyping relation between ground object types , i.e., ones with no type variables ) is the basis for defining the full OO subtyping relation ( i.e., that includes type variables ).
Edit intent: fluency
Original:  In these languages, the subtyping relation between ground object types ( ones with no type variables ) is the basis for defining the full OO subtyping relation ( i.e., that includes type variables ).
Revised:  In these languages, the subtyping relation between ground object types ( ones with no type variables , is the basis for defining the full OO subtyping relation ( i.e., that includes type variables ).
Edit intent: fluency
Original:  In these languages, the subtyping relation between ground object types ( ones with no type variables ) is the basis for defining the full OO subtyping relation ( i.e., that includes type variables ).
Revised:  In these languages, the subtyping relation between ground object types ( ones with no type variables ) is the basis for defining the full OO subtyping relation , i.e., that includes type variables ).
Edit intent: fluency
Original:  We believe the use of this graph operation in constructing the ground generic Java subtyping relation reveals some of the not-immediately-obvious structure of the subtyping relation in generic nominally-typed OO programming languages  .
Revised:  We believe the use of graph operations in constructing the ground generic Java subtyping relation reveals some of the not-immediately-obvious structure of the subtyping relation in generic nominally-typed OO programming languages .
Edit intent: clarity
Original:  Accordingly, we believe that describing precisely how this graph operation is used to construct the subtyping relation of these languages, as we do in this paper, may significantly improve our understanding of  wildcard types and variance annotations in those languages .
Revised:  Accordingly, we believe that describing precisely how this graph operation is used to construct the subtyping relation in these languages, as we do in this paper, may significantly improve our understanding of wildcard types and variance annotations in those languages .
Edit intent: clarity
Original:  In contrast to that we introduce a MH importance sampling estimator which explicitly incorporates all proposed states generated by the MH algorithm.
Revised:  In contrast to that we consider a MH importance sampling estimator which explicitly incorporates all proposed states generated by the MH algorithm.
Edit intent: clarity
Original:  Moreover, although the new estimator uses the same amount of information as the classical MH estimator, it can outperform the latter as indicated by numerical experiments.
Revised:  Moreover, although the analyzed estimator uses the same amount of information as the classical MH estimator, it can outperform the latter as indicated by numerical experiments.
Edit intent: clarity
Original:  However, the rejection of proposals also causes highly correlated samples.
Revised:  However, the rejection of proposals causes highly correlated samples.
Edit intent: clarity
Original:  The estimator satisfies a strong law of large numbers as well as a central limit theorem  and, in addition to that, we provide an explicit mean squared error bound.
Revised:  The estimator satisfies a strong law of large numbers as well as a central limit theorem , and, in addition to that, we provide an explicit mean squared error bound.
Edit intent: fluency
Original: We present a blended conditional gradient approach for minimizing a smooth convex function over a polytope P, that combines the Frank--Wolfe algorithm (also called conditional gradient) with gradient-based steps  different from away steps and pairwise steps, however, still achieving linear convergence for strongly convex functions and good practical performance.
Revised: We present a blended conditional gradient approach for minimizing a smooth convex function over a polytope P, combining the Frank--Wolfe algorithm (also called conditional gradient) with gradient-based steps different from away steps and pairwise steps, however, still achieving linear convergence for strongly convex functions and good practical performance.
Edit intent: coherence
Original: We present a blended conditional gradient approach for minimizing a smooth convex function over a polytope P, that combines the Frank--Wolfe algorithm (also called conditional gradient) with gradient-based steps  different from away steps and pairwise steps, however, still achieving linear convergence for strongly convex functions and good practical performance.
Revised: We present a blended conditional gradient approach for minimizing a smooth convex function over a polytope P, that combines the Frank--Wolfe algorithm (also called conditional gradient) with gradient-based steps , different from away steps and pairwise steps, however, still achieving linear convergence for strongly convex functions and good practical performance.
Edit intent: fluency
Original: We present a blended conditional gradient approach for minimizing a smooth convex function over a polytope P, that combines the Frank--Wolfe algorithm (also called conditional gradient) with gradient-based steps  different from away steps and pairwise steps, however, still achieving linear convergence for strongly convex functions and good practical performance.
Revised: We present a blended conditional gradient approach for minimizing a smooth convex function over a polytope P, that combines the Frank--Wolfe algorithm (also called conditional gradient) with gradient-based steps different from away steps and pairwise steps, but still achieving linear convergence for strongly convex functions and good practical performance.
Edit intent: coherence
Original: We present a blended conditional gradient approach for minimizing a smooth convex function over a polytope P, that combines the Frank--Wolfe algorithm (also called conditional gradient) with gradient-based steps  different from away steps and pairwise steps, however, still achieving linear convergence for strongly convex functions and good practical performance.
Revised: We present a blended conditional gradient approach for minimizing a smooth convex function over a polytope P, that combines the Frank--Wolfe algorithm (also called conditional gradient) with gradient-based steps different from away steps and pairwise steps, however, still achieving linear convergence for strongly convex functions , along with good practical performance.
Edit intent: coherence
Original:  Our approach retains all favorable properties of conditional gradient algorithms, most notably avoidance of projections onto P and maintenance of iterates as sparse convex combinations of a limited number of extreme points of P.
Revised:  Our approach retains all favorable properties of conditional gradient algorithms, notably avoidance of projections onto P and maintenance of iterates as sparse convex combinations of a limited number of extreme points of P.
Edit intent: fluency
Original:  The algorithm  decreases measures of optimality (primal and dual gaps) rapidly, both in the number of iterations and in wall-clock time, outperforming even the efficient "lazified" conditional gradient algorithms of [arXiv:1410.8816].
Revised:  The algorithm decreases measures of optimality (primal and dual gaps) rapidly, both in the number of iterations and in wall-clock time, outperforming even the lazy conditional gradient algorithms of [arXiv:1410.8816].
Edit intent: clarity
Original:  We also present a streamlined algorithm when P is the probability simplex.
Revised:  We also present a streamlined version of the algorithm for the probability simplex.
Edit intent: clarity
Original:  This allows us to incorporate any available prior knowledge in a fully explicit way.
Edit intent: coherence
Original:  Finally, we provide a real-market test of the proposed option-based indicator  .
Revised:  Finally, we provide real-market test of the proposed option-based indicator .
Edit intent: fluency
Original:  Finally, we provide a real-market test of the proposed option-based indicator  .
Revised:  Finally, we provide a real-market tests of the proposed option-based indicator .
Edit intent: fluency
Original:  We define 12 classes of logic programs that exemplify increased level of complexity of the inference process ( multi-hop and default reasoning ) and show that our NIN passes 10 out of the 12 tasks.
Revised:  We define 12 classes of logic programs exemplifying increased level of complexity of the inference process ( multi-hop and default reasoning ) and show that our NIN passes 10 out of the 12 tasks.
Edit intent: fluency
Original:  Hence , the detection of these communities may be aided through the use of measures of the local "richness" of cyclic structures.
Revised:  Thus , the detection of these communities may be aided through the use of measures of the local "richness" of cyclic structures.
Edit intent: fluency
Original:  Hence , the detection of these communities may be aided through the use of measures of the local "richness" of cyclic structures.
Revised:  Hence , the detection of these communities may be aided through the incorporation of measures of the local "richness" of cyclic structures.
Edit intent: clarity
Original:  We argue that RNBRW provides an efficient and scalable alternative to LM . We give simulation results that suggest pre-weighting edges by the proposed methods can improve the performance of popular community detection algorithms substantially.
Revised:  We argue that RNBRW provides an efficient and scalable alternative to LM . We give simulation results showing that pre-weighting edges by the proposed methods can improve the performance of popular community detection algorithms substantially.
Edit intent: clarity