wanyu/IteraTeR_v2 huggingface dataset:
Original:  (b) while colimits always exist in%DIFDELCMD < {\bf %%% iE , it is not the case for%DIFDELCMD < {\bf %%% iC and%DIFDELCMD < {\bf %%% iB ;
Revised:  (b) while colimits always exist in%DIFDELCMD < {\bf %%% , it is not the case for%DIFDELCMD < {\bf %%% iC and%DIFDELCMD < {\bf %%% iB ;
Edit intent: coherence
Original:  (b) while colimits always exist in%DIFDELCMD < {\bf %%% iE , it is not the case for%DIFDELCMD < {\bf %%% iC and%DIFDELCMD < {\bf %%% iB ;
Revised:  (b) while colimits always exist in%DIFDELCMD < {\bf %%% iE %DIFDELCMD < {\bf %%% iC and%DIFDELCMD < {\bf %%% iB ;
Edit intent: coherence
Original:  (b) while colimits always exist in%DIFDELCMD < {\bf %%% iE , it is not the case for%DIFDELCMD < {\bf %%% iC and%DIFDELCMD < {\bf %%% iB ;
Revised:  (b) while colimits always exist in%DIFDELCMD < {\bf %%% iE , it is not the case for%DIFDELCMD < {\bf %%% and%DIFDELCMD < {\bf %%% iB ;
Edit intent: fluency
Original:  (b) while colimits always exist in%DIFDELCMD < {\bf %%% iE , it is not the case for%DIFDELCMD < {\bf %%% iC and%DIFDELCMD < {\bf %%% iB ;
Revised:  (b) while colimits always exist in%DIFDELCMD < {\bf %%% iE , it is not the case for%DIFDELCMD < {\bf %%% iC %DIFDELCMD < {\bf %%% iB ;
Edit intent: coherence
Original:  (b) while colimits always exist in%DIFDELCMD < {\bf %%% iE , it is not the case for%DIFDELCMD < {\bf %%% iC and%DIFDELCMD < {\bf %%% iB ;
Revised:  (b) while colimits always exist in%DIFDELCMD < {\bf %%% iE , it is not the case for%DIFDELCMD < {\bf %%% iC and%DIFDELCMD < {\bf %%% ;
Edit intent: clarity
Original:  Recently, we proposed a new automated which uses renormalized Levenshtein (or edit) distance among words with the same meaning and averaging on the words contained in a list.
Revised:  Recently, we proposed a new automated method which uses normalized Levenshtein distance among words with the same meaning and averaging on the words contained in a list.
Edit intent: clarity
Original:  Recently, we proposed a new automated which uses renormalized Levenshtein (or edit) distance among words with the same meaning and averaging on the words contained in a list.
Revised:  Recently, we proposed a new automated which uses renormalized Levenshtein (or edit) distance among words with the same meaning and averages on the words contained in a list.
Edit intent: fluency
Original:  This problem is tackled here by an automated methodology only based on renormalized Levenshtein distance.
Revised:  This problem is tackled here by an automated methodology only based on normalized Levenshtein distance.
Edit intent: fluency
Original: Using the quantum cavity method, we present an analytical study of the phase diagram of a random optimization problem in a transverse field, in the thermodynamic limit and for a uniformly random distribution of instances.
Revised: We present a study of the phase diagram of a random optimization problem in a transverse field, in the thermodynamic limit and for a uniformly random distribution of instances.
Edit intent: clarity
Original:  We back up our results with Quantum Monte Carlo and Exact Diagonalization methods, and provide evidence that the gap vanishes exponentially with the system size at the transition.
Revised:  We provide evidence that the gap vanishes exponentially with the system size at the transition.
Edit intent: coherence
Original:  This suggests that the Quantum Adiabatic Algorithm requires an exponential time to find the ground state of such problems .
Revised:  This indicates that the Quantum Adiabatic Algorithm requires an exponential time to find the ground state of such problems .
Edit intent: clarity
Original:  This suggests that the Quantum Adiabatic Algorithm requires an exponential time to find the ground state of such problems .
Revised:  This suggests that the Quantum Adiabatic Algorithm requires an exponential time to find the ground state of this problem .
Edit intent: clarity
Original:  We apply this modeling to different linear integrate-and-fire neuron models with or without noise synaptic integration, different types of synapses, with possibly transmission delays and absolute and relative refractory period , and this way generalize results previously obtained in certain particular cases (Reutimann, Giugliano et al 2003, Turova Mommaerts et al 1994).
Revised:  We apply this modeling to different linear integrate-and-fire neuron models with or without noise synaptic integration, different types of synapses, possibly featuring noisy synaptic integration, transmission delays and absolute and relative refractory period , and this way generalize results previously obtained in certain particular cases (Reutimann, Giugliano et al 2003, Turova Mommaerts et al 1994).
Edit intent: clarity
Original:  This directly leads to the Possible Winner problem that asks, given a set of partial votes, if a distinguished candidate can still become a winner.
Revised:  This directly leads to the Possible Winner problem that asks, given a set of partial votes, whether a distinguished candidate can still become a winner.
Edit intent: fluency
Original: In [8] conditional full support (CFS) condition was introduced as a sufficient condition for the existence of consistent price systems (CPSs)  . In this note, we give a weaker sufficient condition for a CPS to exist.
Revised: In [8] , a sufficient condition for the existence of consistent price systems (CPSs) . In this note, we give a weaker sufficient condition for a CPS to exist.
Edit intent: coherence
Original: In [8] conditional full support (CFS) condition was introduced as a sufficient condition for the existence of consistent price systems (CPSs)  . In this note, we give a weaker sufficient condition for a CPS to exist.
Revised: In [8] conditional full support (CFS) condition was introduced as a sufficient condition for the existence of consistent price systems (CPSs) was given . In this note, we give a weaker sufficient condition for a CPS to exist.
Edit intent: clarity
Original: In this note, we present a different sufficient condition than theconditional full support condition  (CFS) introduced by Guasoni, R\'asonyi , and Schachermayer [Ann.
Revised: conditional full support condition (CFS) introduced by Guasoni, R\'asonyi , and Schachermayer [Ann.
Edit intent: coherence
Original: In this note, we present a different sufficient condition than theconditional full support condition  (CFS) introduced by Guasoni, R\'asonyi , and Schachermayer [Ann.
Revised: In this note, we present a different sufficient condition than theWe formulate a sufficient condition (CFS) introduced by Guasoni, R\'asonyi , and Schachermayer [Ann.
Edit intent: clarity
Original: In this note, we present a different sufficient condition than theconditional full support condition  (CFS) introduced by Guasoni, R\'asonyi , and Schachermayer [Ann.
Revised: In this note, we present a different sufficient condition than theconditional full support condition (CFS) introduced by Guasoni, Rasonyi , and Schachermayer [Ann.
Edit intent: fluency
Original: All known Markov Chains for sampling a general convex set have mixing times that depend upon the aspect ratio of the convex set, a measure of which is the ratio between the radius of the smallest sphere circumscribed around K and the radius of the largest sphere inscribed in K. Extending earlier work on polytopes, we present a Markov chain  for sampling from a convex body using a self-concordant barrier, whose mixing time does not depend on its aspect ratio or diameter .
Revised: We present a Markov chain for sampling from a convex body using a self-concordant barrier, whose mixing time does not depend on its aspect ratio or diameter .
Edit intent: clarity
Original: All known Markov Chains for sampling a general convex set have mixing times that depend upon the aspect ratio of the convex set, a measure of which is the ratio between the radius of the smallest sphere circumscribed around K and the radius of the largest sphere inscribed in K. Extending earlier work on polytopes, we present a Markov chain  for sampling from a convex body using a self-concordant barrier, whose mixing time does not depend on its aspect ratio or diameter .
Revised: All known Markov Chains for sampling a general convex set have mixing times that depend upon the aspect ratio of the convex set, a measure of which is the ratio between the radius of the smallest sphere circumscribed around K and the radius of the largest sphere inscribed in K. Extending earlier work on polytopes, we present a Markov chain for sampling from a convex body equipped with a self-concordant barrier, whose mixing time does not depend on its aspect ratio or diameter .
Edit intent: clarity
Original:  Whether the body is in isotropic position or not, if it is the intersection of O(n^{1 - \eps) ellipsoids or the feasible set corresponding to semi-definite constraints of rank O(n^{1-\eps}), the bounds on the mixing time improve upon existing bounds.
Revised:  ) ellipsoids or the feasible set corresponding to semi-definite constraints of rank O(n^{1-\eps}), the bounds on the mixing time improve upon existing bounds.
Edit intent: clarity
Original:  On every convex set of dimension n, there exists a self-concordant barrier whose "complexity parameter " is bounded above by O(n) . Consequently, a rapidly mixing Markov chain of the kind we describe can be defined on any convex set.
Revised:  On every convex set of dimension n, there exists a self-concordant barrier whose "complexity " is bounded above by O(n) . Consequently, a rapidly mixing Markov chain of the kind we describe can be defined on any convex set.
Edit intent: clarity
Original:  On every convex set of dimension n, there exists a self-concordant barrier whose "complexity parameter " is bounded above by O(n) . Consequently, a rapidly mixing Markov chain of the kind we describe can be defined on any convex set.
Revised:  On every convex set of dimension n, there exists a self-concordant barrier whose "complexity parameter " is polynomially bounded . Consequently, a rapidly mixing Markov chain of the kind we describe can be defined on any convex set.
Edit intent: clarity
Original:  We use these results to design an algorithm consisting of a single random walk for optimizing a linear functional on a convex set.
Revised:  We use these results to design an algorithm consisting of a single random walk for optimizing a linear function on a convex set.
Edit intent: fluency
Original:  Using results of Barthe barthe and Bobkov and Houdr\'{e , on the isoperimetry of products of (weighted) Riemannian manifolds, we obtain sharper upper bounds on the mixing time of Dikin walk on products of convex sets than the bounds obtained from a direct application of the Localization Lemma, on which, since ( Lov\'{a and Simonovits), the analyses of all random walks on convex sets have relied.
Revised:  Using results of Barthe barthe and Bobkov and Houdr\'e , on the isoperimetry of products of (weighted) Riemannian manifolds, we obtain sharper upper bounds on the mixing time of Dikin walk on products of convex sets than the bounds obtained from a direct application of the Localization Lemma, on which, since ( Lov\'{a and Simonovits), the analyses of all random walks on convex sets have relied.
Edit intent: fluency
Original:  Using results of Barthe barthe and Bobkov and Houdr\'{e , on the isoperimetry of products of (weighted) Riemannian manifolds, we obtain sharper upper bounds on the mixing time of Dikin walk on products of convex sets than the bounds obtained from a direct application of the Localization Lemma, on which, since ( Lov\'{a and Simonovits), the analyses of all random walks on convex sets have relied.
Revised:  Using results of Barthe barthe and Bobkov and Houdr\'{e , on the isoperimetry of products of (weighted) Riemannian manifolds, we obtain sharper upper bounds on the mixing time of Dikin walk on products of convex sets than the bounds obtained from a direct application of the Localization Lemma, on which, since ( Lov\'asz and Simonovits), the analyses of all random walks on convex sets have relied.
Edit intent: fluency
Original: Within the PDE model of tumour-immune dynamics , with angiogenesis taken into account the effects of single photodynamic impact are considered.
Revised: The system of partial differential equations describing tumor-immune dynamics with angiogenesis taken into account the effects of single photodynamic impact are considered.
Edit intent: clarity
Original:  Unlike the strong im-mune response, the stimulation of weak immune response by transient PDT turns out to be insufficient to reduce the tumour.
Revised:  Unlike the strong im-mune response, the stimulation of weak immune response is shown to be insufficient to reduce the tumour.
Edit intent: clarity
Original:  These facts indicate the important role of anti cancer immune response in the long-term tumour control after PDT.
Revised:  These facts indicate the important role of anti-cancer immune response in the long-term tumour control after PDT.
Edit intent: fluency
Original:  These facts indicate the important role of anti cancer immune response in the long-term tumour control after PDT.
Revised:  These facts indicate the important role of anti cancer immune response in the long-term tumor control after PDT.
Edit intent: fluency
Original:  In this article, we perform an in-depth longitudinal analysis of a fairly small network of scientific collaboration (N = 291) constructed from the bibliographic record of a research center involved in the development and application of sensor network  technologies.
Revised:  In this article, we perform an in-depth longitudinal analysis of a relatively small network of scientific collaboration (N = 291) constructed from the bibliographic record of a research center involved in the development and application of sensor network technologies.
Edit intent: clarity
Original:  We then support our preliminary statistical analysis with an in-depth temporal investigation of the assortativity mixing of these node characteristics: academic department, affiliation, position, and country of origin, unveiling the researchers' propensity to collaborate preferentially with others with similar characteristics .
Revised:  We then support our preliminary statistical analysis with an in-depth temporal investigation of the assortative mixing of selected node characteristics, unveiling the researchers' propensity to collaborate preferentially with others with similar characteristics .
Edit intent: clarity
Original:  We then support our preliminary statistical analysis with an in-depth temporal investigation of the assortativity mixing of these node characteristics: academic department, affiliation, position, and country of origin, unveiling the researchers' propensity to collaborate preferentially with others with similar characteristics .
Revised:  We then support our preliminary statistical analysis with an in-depth temporal investigation of the assortativity mixing of these node characteristics: academic department, affiliation, position, and country of origin, unveiling the researchers' propensity to collaborate preferentially with others with a similar academic profile .
Edit intent: clarity
Original:    Moreover, the relatively unexplored issue of the security impact of sensor node compromises on multidimensional queries is studied;
Revised:  prime aggregation Moreover, the relatively unexplored issue of the security impact of sensor node compromises on multidimensional queries is studied;
Edit intent: fluency
Original:  We\emph{  also explore methods of efficiently mitigating the threat of sensor node compromises.
Revised:  We\emph{ , we also explore methods of efficiently mitigating the threat of sensor node compromises.
Edit intent: fluency
Original: For an increasing monotone graph property \mP the local resilience of a graph G with respect to \mP is the minimal r for which there exists of a subgraph H\subseteq G with all degrees at most r such that the removal of the edges of H from G creates a graph that does not possess \mP.
Revised: For an increasing monotone graph property \mP the local resilience of a graph G with respect to \mP is the minimal r for which there exists of a subgraph H\subseteq G with all degrees at most r such that the removal of the edges of H from G creates a graph that does not possesses \mP.
Edit intent: fluency
Original:  In particular we prove that for every positive \varepsilon and large enough values of d with high probability the local resilience of the random d-regular graph \GND with respect to being Hamiltonian is at least (1- \varepsilon )d/6. Using the same ideas we also prove a similar result for the Binomial random graph model ,
Revised:  In particular we prove that for every positive \epsilon and large enough values of d with high probability the local resilience of the random d-regular graph \GND with respect to being Hamiltonian is at least (1- \varepsilon )d/6. Using the same ideas we also prove a similar result for the Binomial random graph model ,
Edit intent: clarity
Original:  In particular we prove that for every positive \varepsilon and large enough values of d with high probability the local resilience of the random d-regular graph \GND with respect to being Hamiltonian is at least (1- \varepsilon )d/6. Using the same ideas we also prove a similar result for the Binomial random graph model ,
Revised:  In particular we prove that for every positive \varepsilon and large enough values of d with high probability the local resilience of the random d-regular graph ,\GND with respect to being Hamiltonian is at least (1- \varepsilon )d/6. Using the same ideas we also prove a similar result for the Binomial random graph model ,
Edit intent: fluency
Original:  In particular we prove that for every positive \varepsilon and large enough values of d with high probability the local resilience of the random d-regular graph \GND with respect to being Hamiltonian is at least (1- \varepsilon )d/6. Using the same ideas we also prove a similar result for the Binomial random graph model ,
Revised:  In particular we prove that for every positive \varepsilon and large enough values of d with high probability the local resilience of the random d-regular graph \GND, with respect to being Hamiltonian is at least (1- \varepsilon )d/6. Using the same ideas we also prove a similar result for the Binomial random graph model ,
Edit intent: fluency
Original:  In particular we prove that for every positive \varepsilon and large enough values of d with high probability the local resilience of the random d-regular graph \GND with respect to being Hamiltonian is at least (1- \varepsilon )d/6. Using the same ideas we also prove a similar result for the Binomial random graph model ,
Revised:  In particular we prove that for every positive \varepsilon and large enough values of d with high probability the local resilience of the random d-regular graph \GND with respect to being Hamiltonian is at least (1- \varepsilon )d/6. We also prove that for the Binomial random graph model ,
Edit intent: clarity
Original:  namely that \GNP for every positive \varepsilon and large enough values of K if p\geq K\ln n{n} then with hight probability the local resilience of \GNP with respect to being Hamiltonian is at least (1- \varepsilon )np/6. 
Revised:  namely that \GNP, for every positive \varepsilon and large enough values of K if p\geq K\ln n{n} then with hight probability the local resilience of \GNP with respect to being Hamiltonian is at least (1- \varepsilon )np/6. 
Edit intent: fluency
Original:  namely that \GNP for every positive \varepsilon and large enough values of K if p\geq K\ln n{n} then with hight probability the local resilience of \GNP with respect to being Hamiltonian is at least (1- \varepsilon )np/6. 
Revised:  namely that \GNP for every positive \varepsilon and large enough values of K if p\geq K\ln n{n} then with high probability the local resilience of \GNP with respect to being Hamiltonian is at least (1- \varepsilon )np/6. 
Edit intent: fluency
Original:  This NP-hard problem belongs to a general class of vertex deletion problems including the vertex cover problem and the feedback vertex set problem.
Edit intent: coherence
Original:  Moreover, we show that the integrality gap of the natural LP relaxation of the problem is \Theta( log n), where n denotes the number of vertices in the graph.
Revised:  Moreover, we show that the integrality gap of the natural LP relaxation of the problem is \Theta( \log n), where n denotes the number of vertices in the graph.
Edit intent: fluency
Original: An edge coloring of a graph G with colors 1,2, ... ,t is called an interval t-coloring if for each i\in \{1,2, ... ,t\} there is at least one edge of G colored by i,  the colors of edges incident to any vertex of G are distinct and form an interval of integers.
Revised: An edge coloring of a graph G with colors 1,2, ... ,t is called an interval t-coloring if for each i\in \{1,2, ... ,t\} there is at least one edge of G colored by i, and the colors of edges incident to any vertex of G are distinct and form an interval of integers.
Edit intent: coherence
Original:  A graph G is interval colorable, if there is  t\geq 1 , for which G has an interval t-coloring.
Revised:  A graph G is interval colorable, if there is an integer t\geq 1 , for which G has an interval t-coloring.
Edit intent: clarity
Original:  A graph G is interval colorable, if there is  t\geq 1 , for which G has an interval t-coloring.
Revised:  A graph G is interval colorable, if there is t\geq 1 for which G has an interval t-coloring.
Edit intent: fluency
Original: We study ensembles of codes on graphs (generalized low-density parity-check, or LDPC codes) and their extension to codes on hypergraphs constructed from random graphs and fixed local constraint codes .
Revised: We study ensembles of codes on graphs (generalized low-density parity-check, or LDPC codes) constructed from random graphs and fixed local constraint codes .
Edit intent: clarity
Original: We study ensembles of codes on graphs (generalized low-density parity-check, or LDPC codes) and their extension to codes on hypergraphs constructed from random graphs and fixed local constraint codes .
Revised: We study ensembles of codes on graphs (generalized low-density parity-check, or LDPC codes) and their extension to codes on hypergraphs constructed from random graphs and fixed local constrained codes, and their extension to codes on hypergraphs .
Edit intent: coherence
Original:  It is known that the  minimum distance of codes in these ensembles grows linearly with the code length.
Revised:  It is known that the average minimum distance of codes in these ensembles grows linearly with the code length.
Edit intent: fluency
Original:  We show that these codes  correct a linearly growing number of errors under simple iterative decoding algorithms.
Revised:  We show that these codes can correct a linearly growing number of errors under simple iterative decoding algorithms.
Edit intent: clarity
Original: This paper focuses on methods to study patterns of collaboration in co-authorship networks at the mesocopic level.
Revised: This paper focuses on methods to study patterns of collaboration in co-authorship networks at the mesoscopic level.
Edit intent: clarity
Original:  The operating principle underlying transient gene expression activity is compared with similar principles governing transient gene expression dynamics in other organisms .
Revised:  We also compare the mechanism of pulse formation with the known mechanisms of pulse generation in some bacterial and viral systems .
Edit intent: clarity
Original:  Considering all the non-redundant protein structures across all the major structural classes, the present study attempts to find the probabilistic distributions that describe several facets of the occurrence of these rare secondary structures in proteins.
Revised:  Considering all the non-redundant protein structures across different structural classes, the present study attempts to find the probabilistic distributions that describe several facets of the occurrence of these rare secondary structures in proteins.
Edit intent: clarity