wanyu/IteraTeR_v2 huggingface dataset:
Original:  We illustrate how CMABFAS could be used to design a fully self-learning SPIT filter that does not rely on feedback from the end-user (i.e., does not require labeled data) and report convincing simulation results.
Revised:  We illustrate how CMABFAS could be used to design a fully self-learning SPIT filter that does not rely on feedback from the end-user (i.e., does not require labeled data) and report first simulation results.
Edit intent: clarity
Original:  Employing the result of this paper together with some other results on polynomial-time homology, which we intend to present in another paper , we hope to obtain, for every fixed k, a polynomial-time algorithm for computing the k-th homotopy group \pi _k(X) of a given simply connected space X, as well as the first k stages of a Postnikov system for X, and also a polynomial-time version of the algorithm of Cadek et al. mentioned above.
Revised:  Employing the result of this paper together with some other results on polynomial-time homology, in another paper , we hope to obtain, for every fixed k, a polynomial-time algorithm for computing the k-th homotopy group \pi _k(X) of a given simply connected space X, as well as the first k stages of a Postnikov system for X, and also a polynomial-time version of the algorithm of Cadek et al. mentioned above.
Edit intent: clarity
Original:  Employing the result of this paper together with some other results on polynomial-time homology, which we intend to present in another paper , we hope to obtain, for every fixed k, a polynomial-time algorithm for computing the k-th homotopy group \pi _k(X) of a given simply connected space X, as well as the first k stages of a Postnikov system for X, and also a polynomial-time version of the algorithm of Cadek et al. mentioned above.
Revised:  Employing the result of this paper together with some other results on polynomial-time homology, which we intend to present in another paper we obtain, for every fixed k, a polynomial-time algorithm for computing the k-th homotopy group \pi _k(X) of a given simply connected space X, as well as the first k stages of a Postnikov system for X, and also a polynomial-time version of the algorithm of Cadek et al. mentioned above.
Edit intent: clarity
Original:  Employing the result of this paper together with some other results on polynomial-time homology, which we intend to present in another paper , we hope to obtain, for every fixed k, a polynomial-time algorithm for computing the k-th homotopy group \pi _k(X) of a given simply connected space X, as well as the first k stages of a Postnikov system for X, and also a polynomial-time version of the algorithm of Cadek et al. mentioned above.
Revised:  Employing the result of this paper together with some other results on polynomial-time homology, which we intend to present in another paper , we hope to obtain, for every fixed k, a polynomial-time algorithm for computing the k-th homotopy group pi _k(X) of a given simply connected space X, as well as the first k stages of a Postnikov system for X, and also a polynomial-time version of the algorithm of Cadek et al. mentioned above.
Edit intent: clarity
Original:  The construction is purely combinatorial and it can be understood as a certain procedure for reducing finite sequences of integers, without any reference to topologyThe Eilenberg--MacLane spaces are the basic building blocks in a Postnikov system, which is a "layered" representation of a topological space suitable for homotopy-theoretic computations.
Revised:  The construction is purely combinatorial and it can be understood as a certain procedure for reducing finite sequences of integers, without any reference to topology.The Eilenberg-MacLane spaces are the basic building blocks in a Postnikov system, which is a "layered" representation of a topological space suitable for homotopy-theoretic computations.
Edit intent: fluency
Original:  For a fixed set of matrices, a sequence of matrices drawn from that set is called extremal if the associated sequence of partial products achieves this maximal rate of growth.
Revised:  For a fixed set of matrices, a sequence of matrices drawn from that set is called extremal if the associated sequence of partial products achieves this maximal rate of growth.
Edit intent: fluency
Original: Let %DIFDELCMD < \R %%%  be a real closed field and %DIFDELCMD < \D %%% \subset%DIFDELCMD < \R %%%  \subset R } an ordered domain.
Revised: Let %DIFDELCMD < \R %%% be a real closed field and %DIFDELCMD < \D %%% %DIFDELCMD < \R %%% \subset R } an ordered domain.
Edit intent: fluency
Original:  The complexity of the algorithm, measured by the number of arithmetic operations in the domain%DIFDELCMD < \D%%%  , is bounded by d^{O(k k)}, where d = deg (Q)\ge 2.
Revised:  The complexity of the algorithm, measured by the number of arithmetic operations in the %DIFDELCMD < \D%%% , is bounded by d^{O(k k)}, where d = deg (Q)\ge 2.
Edit intent: clarity
Original:  The best previously known algorithm for constructing a roadmap of a real algebraic subset of %DIFDELCMD < \R%%%  ^k defined by a polynomial of degree d had complexity d^{O(k^2)}.
Revised:  The best previously known algorithm for constructing a roadmap of a real algebraic subset of %DIFDELCMD < \R%%% ^k defined by a polynomial of degree d has complexity d^{O(k^2)}.
Edit intent: fluency
Original:  We have found that arsenate is not needed for growth of GFAJ-1 when phosphate is limiting .
Revised:  However, we have found that arsenate is not needed for growth of GFAJ-1 when phosphate is limiting .
Edit intent: coherence
Original:  We have found that arsenate is not needed for growth of GFAJ-1 when phosphate is limiting .
Revised:  We have found that arsenate does not contribute to growth of GFAJ-1 when phosphate is limiting .
Edit intent: clarity
Original:   Among both the theoretical and the real networks considered, we observe  high correlation between the total epidemic prevalence and the degree,  the strength and the accessibility of the epidemic sources.
Revised:  Among both the theoretical and the real networks considered, we observe a high correlation between the total epidemic prevalence and the degree, the strength and the accessibility of the epidemic sources.
Edit intent: fluency
Original:   Among both the theoretical and the real networks considered, we observe  high correlation between the total epidemic prevalence and the degree,  the strength and the accessibility of the epidemic sources.
Revised:  Among both the theoretical and the real networks considered, we observe high correlation between the total epidemic prevalence and the degree, as well as the strength and the accessibility of the epidemic sources.
Edit intent: coherence
Original: Dengue viral infections show unique infection patterns arising from its four serotypes , (DENV-1,2,3,4).
Revised: Dengue viral infections show unique infection patterns arising from its four serot- ypes , (DENV-1,2,3,4).
Edit intent: fluency
Original:  The models  incorporate time delays, antibody dependent enhancement (ADE), a dynamic switch and a correlation factor between different DENV serotypes.
Revised:  The models presented here incorporate time delays, antibody dependent enhancement (ADE), a dynamic switch and a correlation factor between different DENV serotypes.
Edit intent: clarity
Original:  Stability analysis of the model shows interesting dependence on the time delays .
Revised:  Stability analysis of the model shows interesting dependence on the time delay involved in the production of antibodies from plasma cells .
Edit intent: clarity
Original:  For secondary infections of a different serotype, the homologous antibody production is enhanced due to the influence of heterologous antibodies and is also controlled by the correlation factor,  a measure of similarities between the different DENV serotypes involved , introduced in this work.
Revised:  For secondary infections with a different serotype, the homologous antibody production is enhanced due to the influence of heterologous antibodies and is also controlled by the correlation factor, a measure of similarities between the different DENV serotypes involved , introduced in this work.
Edit intent: clarity
Original:  For secondary infections of a different serotype, the homologous antibody production is enhanced due to the influence of heterologous antibodies and is also controlled by the correlation factor,  a measure of similarities between the different DENV serotypes involved , introduced in this work.
Revised:  For secondary infections of a different serotype, the homologous antibody production is enhanced due to the influence of heterologous antibodies . The antibody production is also controlled by the correlation factor, a measure of similarities between the different DENV serotypes involved , introduced in this work.
Edit intent: coherence
Original:  For secondary infections of a different serotype, the homologous antibody production is enhanced due to the influence of heterologous antibodies and is also controlled by the correlation factor,  a measure of similarities between the different DENV serotypes involved , introduced in this work.
Revised:  For secondary infections of a different serotype, the homologous antibody production is enhanced due to the influence of heterologous antibodies and is also controlled by the correlation factor, which is a measure of similarities between the different DENV serotypes involved , introduced in this work.
Edit intent: coherence
Original: In this paper we study the generating functionals of several models of random packing processes: the classical Mat\'ern hard-core model;
Revised: In this paper we study the generating functionals of several random packing processes: the classical Mat\'ern hard-core model;
Edit intent: clarity
Original:  The main new results are: 1) a sufficient condition for the \infty-Mat\'ern model to be well-defined (unlike the other two, the \infty-Mat\'ern model may not be well-defined on unbounded spaces) ;
Revised:  We first give a sufficient condition for the \infty-Mat\'ern model to be well-defined (unlike the other two, the \infty-Mat\'ern model may not be well-defined on unbounded spaces) ;
Edit intent: coherence
Original:  The main new results are: 1) a sufficient condition for the \infty-Mat\'ern model to be well-defined (unlike the other two, the \infty-Mat\'ern model may not be well-defined on unbounded spaces) ;
Revised:  The main new results are: 1) a sufficient condition for the \infty-Mat\'ern model to be well-defined (unlike the other two, the latter may not be well-defined on unbounded spaces) ;
Edit intent: clarity
Original:  2) the generating functional of the resulting point process which is given for each of the three models as the solution of a differential equation ;
Revised:  2) the generating functional of the resulting point process is given for each of the three models as the solution of a differential equation ;
Edit intent: clarity
Original:  4) moment measures and other useful properties of the considered packing models which are derived from their generating functionals .
Revised:  4) moment measures and Palm distributions of the considered packing models which are derived from their generating functionals .
Edit intent: clarity
Original:  4) moment measures and other useful properties of the considered packing models which are derived from their generating functionals .
Revised:  4) moment measures and other useful properties of the considered packing models departing from their generating functionals .
Edit intent: clarity
Original: Let G be a directed graph with n vertices and non-negative weights in its directed edges, embedded on a surface of genus g, and let F be an arbitrary face of G. We describe an algorithm to preprocess the graph in O(gn log n) time  , so that the shortest-path distance from any vertex on the boundary of F to any other vertex in G can be retrieved in O(log n) time.
Revised: Let G be a directed graph with n vertices and non-negative weights in its directed edges, embedded on a surface of genus g, and let F be an arbitrary face of G. We describe an algorithm to preprocess the graph in O(gn log n) time , so that the shortest-path distance from any vertex on the boundary of f to any other vertex in G can be retrieved in O(log n) time.
Edit intent: clarity
Original:  Intuitively, our preprocessing algorithm maintains a shortest-path tree as its source point moves continuously around the boundary of F . As an application of our algorithm, we describe algorithms to compute a shortest non-contractible or non-separating cycle in embedded, undirected graphs in O(g^2 n log n) time  .
Revised:  Intuitively, our preprocessing algorithm maintains a shortest-path tree as its source point moves continuously around the boundary of f . As an application of our algorithm, we describe algorithms to compute a shortest non-contractible or non-separating cycle in embedded, undirected graphs in O(g^2 n log n) time .
Edit intent: clarity
Original:  They claim to have discovered a class of graphs (called "superstars"), with a parameter k , within which the probability of fixation tends to 1-r^{-k} as graphs get larger .
Revised:  They describe a class of graphs (called "superstars"), with a parameter k , within which the probability of fixation tends to 1-r^{-k} as graphs get larger .
Edit intent: clarity
Original:  Since the claimed proof is flawed, and no others are known, we investigate the claim via simulation.
Revised:  We do believe that the qualitative claim of
Edit intent: clarity
Original:  We propose a generalization of Schnyder woods to toroidal maps with application to graph drawing.
Revised:  We propose a generalization of Schnyder woods to graphs embedded on the torus with application to graph drawing.
Edit intent: clarity
Original:  We prove the existence of these Schnyder woods for toroidal triangulations .
Revised:  We prove several properties on this new object. Among all we prove that a graph embedded on the torus admits such a Schnyder wood if and only if it is an essentially 3-connected toroidal map .
Edit intent: coherence
Original:  We show that  Schnyder woods can be used to embed the universal cover of a toroidal map on an infinite and periodic orthogonal surface.
Revised:  We show that these Schnyder woods can be used to embed the universal cover of a toroidal map on an infinite and periodic orthogonal surface.
Edit intent: clarity
Original: In this article we propose a method for non-linear fitting that incorporates some of the features of linear least squares into a general minimum \chi^2 fit . Given a fitting function f(x)depending linearly on parameters \{a _i\} and non-linearly on the parameters \{b_i\}, the proposed method allows to reduce the space of the fitting parameters to the \{b_i\} only by determining the \{a _i\ performed tests of the algorithm using simulated data.
Revised: In this notes we describe an algorithm for non-linear fitting that incorporates some of the features of linear least squares into a general minimum \chi^2 fit . Given a fitting function f(x)depending linearly on parameters \{a _i\} and non-linearly on the parameters \{b_i\}, the proposed method allows to reduce the space of the fitting parameters to the \{b_i\} only by determining the \{a _i\ performed tests of the algorithm using simulated data.
Edit intent: clarity
Original: In this article we propose a method for non-linear fitting that incorporates some of the features of linear least squares into a general minimum \chi^2 fit . Given a fitting function f(x)depending linearly on parameters \{a _i\} and non-linearly on the parameters \{b_i\}, the proposed method allows to reduce the space of the fitting parameters to the \{b_i\} only by determining the \{a _i\ performed tests of the algorithm using simulated data.
Revised: In this article we propose a method for non-linear fitting which incorporates some of the features of linear least squares into a general minimum \chi^2 fit . Given a fitting function f(x)depending linearly on parameters \{a _i\} and non-linearly on the parameters \{b_i\}, the proposed method allows to reduce the space of the fitting parameters to the \{b_i\} only by determining the \{a _i\ performed tests of the algorithm using simulated data.
Edit intent: fluency
Original: We generalize the theory of Cellular Automata to arbitrary, time-varying graphs.
Revised: We extend the theory of Cellular Automata to arbitrary, time-varying graphs.
Edit intent: clarity
Original:  In other words we formalize, and prove theorems about, the intuitive idea of a labelled graph which evolves in time - but under the natural constraint that information can only ever be transmitted at a bounded speed, with respect to the distance given by the graph.
Revised:  In other words we formalize, and prove theorems about, the intuitive idea of a labelled graph which evolves in time --- but under the natural constraint that information can only ever be transmitted at a bounded speed, with respect to the distance given by the graph.
Edit intent: fluency
Original:  In the finite case some fundamental facts of Cellular Automata theory carry through: causal graph dynamics admit a characterization as continuous functions  and they are stable under inversion.
Revised:  In the finite case some fundamental facts of Cellular Automata theory carry through: causal graph dynamics admit a characterization as continuous functions , and they are stable under inversion.
Edit intent: fluency
Original:  In other words we formalize, and prove theorems about, the intuitive idea of a labelled graph which evolves in time --- but under the natural constraint that information can only ever be transmitted at a bounded speed, with respect to the distance given by the graph.
Revised:  In other words we formalize, and prove theorems about, the intuitive idea of a labelled graph which evolves in time - but under the natural constraint that information can only ever be transmitted at a bounded speed, with respect to the distance given by the graph.
Edit intent: fluency
Original:  The definition we provide for these ` causal graph dynamics ' is simple and axiomatic.
Revised:  The definition we provide for these " causal graph dynamics ' is simple and axiomatic.
Edit intent: fluency
Original:  The definition we provide for these ` causal graph dynamics ' is simple and axiomatic.
Revised:  The definition we provide for these ` causal graph dynamics " is simple and axiomatic.
Edit intent: fluency
Original:  Keywords : Dynamical networks, Boolean networks, Generative networks automata, Cayley cellular automata, Graph Automata, Graph rewriting automata, Parallel graph transformations, Amalgamated graph transformations, Hedlund , Regge calculus, Local, No-signalling.
Revised:  KEYWORDS : Dynamical networks, Boolean networks, Generative networks automata, Cayley cellular automata, Graph Automata, Graph rewriting automata, Parallel graph transformations, Amalgamated graph transformations, Hedlund , Regge calculus, Local, No-signalling.
Edit intent: fluency
Original: MicroRNA can affect the protein translation using nine mechanistically different mechanisms, including repression of initiation and degradation of the transcript.
Revised: MicroRNAs can affect the protein translation using nine mechanistically different mechanisms, including repression of initiation and degradation of the transcript.
Edit intent: fluency
Original:  The worst, same experimental systems dealing with the same pairs of mRNA and miRNA can provide controversial evidences about which is the actual mechanism of translation repression observed in the experiment.
Revised:  The worst, same experimental systems dealing with the same pairs of mRNA and miRNA can provide ambiguous evidences about which is the actual mechanism of translation repression observed in the experiment.
Edit intent: clarity
Original:  We start with reviewing the current state of the art about the knowledge of various mechanisms of miRNA action and suggest that mathematical modeling can help resolving some of the controversial interpretations.
Revised:  We start with reviewing the current knowledge of various mechanisms of miRNA action and suggest that mathematical modeling can help resolving some of the controversial interpretations.
Edit intent: clarity
Original:  The actually observed mechanism will be that acting on the limiting step of translation which might vary from one experimental setting to another.
Revised:  The actually observed mechanism will be that acting on or changing the limiting "place" of the translation process. The limiting place can vary from one experimental setting to another.
Edit intent: clarity
Original:  The formula has two versions, the chemical balance version is: equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% ) = \mu_eN_e(%DIFDELCMD < \bX%%% ) + \sum_{i=1^H \mu_i N_i(}%DIFDELCMD < \bX%%% ), equation*%DIFDELCMD < } %DIFDELCMD < %%% where N_e(%DIFDELCMD < \bX%%% ) is the mean number of electrons in the space included by the first hydration shell of%DIFDELCMD < \bX%%% , \mu_e is its chemical potential;
Revised:  equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% ) = \mu_eN_e(%DIFDELCMD < \bX%%% ) + \sum_{i=1^H \mu_i N_i(}%DIFDELCMD < \bX%%% ), equation*%DIFDELCMD < } %DIFDELCMD < %%% where N_e(%DIFDELCMD < \bX%%% ) is the mean number of electrons in the space included by the first hydration shell of%DIFDELCMD < \bX%%% , \mu_e is its chemical potential;
Edit intent: coherence
Original:  The formula has two versions, the chemical balance version is: equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% ) = \mu_eN_e(%DIFDELCMD < \bX%%% ) + \sum_{i=1^H \mu_i N_i(}%DIFDELCMD < \bX%%% ), equation*%DIFDELCMD < } %DIFDELCMD < %%% where N_e(%DIFDELCMD < \bX%%% ) is the mean number of electrons in the space included by the first hydration shell of%DIFDELCMD < \bX%%% , \mu_e is its chemical potential;
Revised:  The formula has two versions, the chemical balance version is: %DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% ) = \mu_eN_e(%DIFDELCMD < \bX%%% ) + \sum_{i=1^H \mu_i N_i(}%DIFDELCMD < \bX%%% ), equation*%DIFDELCMD < } %DIFDELCMD < %%% where N_e(%DIFDELCMD < \bX%%% ) is the mean number of electrons in the space included by the first hydration shell of%DIFDELCMD < \bX%%% , \mu_e is its chemical potential;
Edit intent: fluency
Original:  The formula has two versions, the chemical balance version is: equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% ) = \mu_eN_e(%DIFDELCMD < \bX%%% ) + \sum_{i=1^H \mu_i N_i(}%DIFDELCMD < \bX%%% ), equation*%DIFDELCMD < } %DIFDELCMD < %%% where N_e(%DIFDELCMD < \bX%%% ) is the mean number of electrons in the space included by the first hydration shell of%DIFDELCMD < \bX%%% , \mu_e is its chemical potential;
Revised:  The formula has two versions, the chemical balance version is: equation*%DIFDELCMD < } %%% %DIFDELCMD < \bX%%% ) = \mu_eN_e(%DIFDELCMD < \bX%%% ) + \sum_{i=1^H \mu_i N_i(}%DIFDELCMD < \bX%%% ), equation*%DIFDELCMD < } %DIFDELCMD < %%% where N_e(%DIFDELCMD < \bX%%% ) is the mean number of electrons in the space included by the first hydration shell of%DIFDELCMD < \bX%%% , \mu_e is its chemical potential;
Edit intent: coherence
Original:  The formula has two versions, the chemical balance version is: equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% ) = \mu_eN_e(%DIFDELCMD < \bX%%% ) + \sum_{i=1^H \mu_i N_i(}%DIFDELCMD < \bX%%% ), equation*%DIFDELCMD < } %DIFDELCMD < %%% where N_e(%DIFDELCMD < \bX%%% ) is the mean number of electrons in the space included by the first hydration shell of%DIFDELCMD < \bX%%% , \mu_e is its chemical potential;
Revised:  The formula has two versions, the chemical balance version is: equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% %DIFDELCMD < \bX%%% ) + \sum_{i=1^H \mu_i N_i(}%DIFDELCMD < \bX%%% ), equation*%DIFDELCMD < } %DIFDELCMD < %%% where N_e(%DIFDELCMD < \bX%%% ) is the mean number of electrons in the space included by the first hydration shell of%DIFDELCMD < \bX%%% , \mu_e is its chemical potential;
Edit intent: coherence