wanyu/IteraTeR_v2 huggingface dataset:
Original:  We validate the applicability of MSFN to general integral currents by providing a simplicial approximation theorem, which states that one may approximate such a current with a simplicial current while bounding the expansion of its mass.
Revised:  We validate the applicability of MSFN to general integral currents by providing a simplicial approximation theorem, which states that one may approximate a general current with a simplicial current while bounding the expansion of its mass.
Edit intent: clarity
Original:  As illustrated by our computations, MSFN opens up the possibility of using flat norm to denoise and extract scale information of large data sets in arbitrary dimensions  .
Revised:  As illustrated by our computations, MSFN opens up the possibilities of using flat norm to denoise and extract scale information of large data sets in arbitrary dimensions .
Edit intent: fluency
Original:  As illustrated by our computations, MSFN opens up the possibility of using flat norm to denoise and extract scale information of large data sets in arbitrary dimensions  .
Revised:  As illustrated by our computations, MSFN opens up the possibility of using flat norm to denoise or extract scale information of large data sets in arbitrary dimensions .
Edit intent: fluency
Original: A k-box B=(R_1, R_2, ...,R_k), where each R_i is a closed interval on the real line, is defined to be the Cartesian product R_1\times R_2\times ...\times R_k. If each R_i is a unit length interval, we call B a k-cube.
Revised: A k-box B=(R_1, ...,R_k), where each R_i is a closed interval on the real line, is defined to be the Cartesian product R_1\times R_2\times ...\times R_k. If each R_i is a unit length interval, we call B a k-cube.
Edit intent: fluency
Original:  Boxicity of a graph G, denoted as \boxi(G), is the minimum integer k such that G is an intersection graph of k-boxes.
Revised:  Boxicity of a graph G, denoted as \boxi(G), is the minimum integer k such that G is an intersection graph of k-boxes.
Edit intent: fluency
Original:  Similarly, the cubicity of G, denoted as \cubi(G), is the minimum integer k such that G is an intersection graph of k-cubes.
Revised:  Similarly, the cubicity of G, denoted as \cubi(G), is the minimum integer k such that G is an intersection graph of k-cubes.
Edit intent: coherence
Original:   We also give an efficient deterministic algorithm that runs in O(n^2k) time to output a 8k(\lceil 2.42 \log n\rceil + 1) dimensional cube representation for G. An important consequence of the above result is that if the crossing number of a graph G is t, then \boxi(G) is O(t ^{\1/4 \lceil\log t\rceil}^{3/4}) . This bound is tight upto a factor of O((\log t)^{ 3 /4}).
Revised:  This bound is tight. We also give an efficient deterministic algorithm that runs in O(n^2k) time to output a 8k(\lceil 2.42 \log n\rceil + 1) dimensional cube representation for G. An important consequence of the above result is that if the crossing number of a graph G is t, then \boxi(G) is O(t ^{\1/4 \lceil\log t\rceil}^{3/4}) . This bound is tight upto a factor of O((\log t)^{ 3 /4}).
Edit intent: fluency
Original:   We also give an efficient deterministic algorithm that runs in O(n^2k) time to output a 8k(\lceil 2.42 \log n\rceil + 1) dimensional cube representation for G. An important consequence of the above result is that if the crossing number of a graph G is t, then \boxi(G) is O(t ^{\1/4 \lceil\log t\rceil}^{3/4}) . This bound is tight upto a factor of O((\log t)^{ 3 /4}).
Revised:  We also give an efficient deterministic algorithm that runs in O(n^2k) time to output a 8k(\lceil 2.42 \log n\rceil + 1) dimensional cube representation for G. An important consequence of the above result is that if the crossing number of a graph G is t, then \boxi(G) is O(t ^{1/4 \lceil\log t\rceil}^{3/4}) . This bound is tight upto a factor of O((\log t)^{ 3 /4}).
Edit intent: fluency
Original:   We also give an efficient deterministic algorithm that runs in O(n^2k) time to output a 8k(\lceil 2.42 \log n\rceil + 1) dimensional cube representation for G. An important consequence of the above result is that if the crossing number of a graph G is t, then \boxi(G) is O(t ^{\1/4 \lceil\log t\rceil}^{3/4}) . This bound is tight upto a factor of O((\log t)^{ 3 /4}).
Revised:  We also give an efficient deterministic algorithm that runs in O(n^2k) time to output a 8k(\lceil 2.42 \log n\rceil + 1) dimensional cube representation for G. An important consequence of the above result is that if the crossing number of a graph G is t, then \boxi(G) is O(t ^{\1/4 \lceil\log t\rceil}^{3/4}) . This bound is tight up to a factor of O((\log t)^{ 3 /4}).
Edit intent: fluency
Original:   We also give an efficient deterministic algorithm that runs in O(n^2k) time to output a 8k(\lceil 2.42 \log n\rceil + 1) dimensional cube representation for G. An important consequence of the above result is that if the crossing number of a graph G is t, then \boxi(G) is O(t ^{\1/4 \lceil\log t\rceil}^{3/4}) . This bound is tight upto a factor of O((\log t)^{ 3 /4}).
Revised:  We also give an efficient deterministic algorithm that runs in O(n^2k) time to output a 8k(\lceil 2.42 \log n\rceil + 1) dimensional cube representation for G. An important consequence of the above result is that if the crossing number of a graph G is t, then \boxi(G) is O(t ^{\1/4 \lceil\log t\rceil}^{3/4}) . This bound is tight upto a factor of O((\log t)^{ 1 /4}).
Edit intent: fluency
Original:  Let dim(\mathcal{P}) denote the }\emph{poset dimension of \mathcal{P.
Revised:  Let dim(\mathcal{P}) denote the }\emph{ of \mathcal{P.
Edit intent: clarity
Original:  Let dim(\mathcal{P}) denote the }\emph{poset dimension of \mathcal{P.
Revised:  Let dim(\mathcal{P}) denote the }\emph{poset dimension .
Edit intent: clarity
Original:  Using our bound for the cubicity of k-degenerate graphs we show that cubicity of almost all graphs in \mathcal{G}(n,m) model is O(d_{av}\log n} ) %DIFDELCMD < \lceil %%% 2e \log n%DIFDELCMD < \rceil%%% , where k denotes the degeneracy of G_{\mathcal{P}.
Revised:  Using our bound for the cubicity of k-degenerate graphs we show that cubicity of almost all graphs in \mathcal{G}(n,m) model is O(d_{av}\log n} ) %DIFDELCMD < \lceil %%% %DIFDELCMD < \rceil%%% , where k denotes the degeneracy of G_{\mathcal{P}.
Edit intent: coherence
Original:  We attend to a scenario where some of the routers are anonymous, and propose two fundamental axioms that model two basic assumptions on the traceroute data: (1) each trace corresponds to a real path in the network, and (2) the routing paths are at most a factor 1/ \alpha off the optimal paths, for some parameter \alpha\in (0,1].
Revised:  We attend to a scenario where some of the routers are anonymous, and propose two fundamental axioms that model two basic assumptions on the traceroute data: (1) each trace corresponds to a real path in the network, and (2) the routing paths are at most a factor 1/ alpha off the shortest paths, for some parameter \alpha\in (0,1].
Edit intent: clarity
Original:  We attend to a scenario where some of the routers are anonymous, and propose two fundamental axioms that model two basic assumptions on the traceroute data: (1) each trace corresponds to a real path in the network, and (2) the routing paths are at most a factor 1/ \alpha off the optimal paths, for some parameter \alpha\in (0,1].
Revised:  We attend to a scenario where some of the routers are anonymous, and propose two fundamental axioms that model two basic assumptions on the traceroute data: (1) each trace corresponds to a real path in the network, and (2) the routing paths are at most a factor 1/ \alpha off the optimal paths, for some parameter alpha in (0,1].
Edit intent: fluency
Original: The network reliability problem for evaluating the network failure probability has been extensively studied .
Revised: The network reliability problem for evaluating the network failure probability has been extensively investigated .
Edit intent: clarity
Original:  For a given undirected graph G, the network failure probability is the probability such that edge failures  make G unconnected.
Revised:  For a given undirected graph G, the network failure probability is the probability that edge failures make G unconnected.
Edit intent: clarity
Original:  It is assumed that edge failures occur independently with the same probability.
Revised:  Edge failures are assumed to occur independently with the same probability.
Edit intent: clarity
Original:  We assume a simple random graph model closely related to the Erdos-R\'{e}nyi random graph . By using the fact that the cut-set space of G is a linear space over \Bbb F_2 spanned by the incident matrix of G , we have derived upper and lower bounds on expected network failure probability.
Revised:  We assume a simple random graph ensemble that is closely related to the Erdos-R\'{e}nyi random graph . By using the fact that the cut-set space of G is a linear space over \Bbb F_2 spanned by the incident matrix of G , we have derived upper and lower bounds on expected network failure probability.
Edit intent: clarity
Original: TIn the field of computer science, the network reliability problem for evaluating the network failure probability has been extensively investigated.
Revised: In the field of computer science, the network reliability problem for evaluating the network failure probability has been extensively investigated.
Edit intent: fluency
Original:  Device-free passive (DfP ) indoor localization is an emerging technology enabling the localization of entities that do not carry any devices nor participate actively in the localization process using the already installed wireless infrastructure.
Revised:  Device-free passive DfP indoor localization is an emerging technology enabling the localization of entities that do not carry any devices nor participate actively in the localization process using the already installed wireless infrastructure.
Edit intent: fluency
Original:  This technology is useful for a variety of applications , where special hardware might not be applicable or affordable such as intrusion detection, smart homes and border protection.
Revised:  This technology is useful for a variety of applications such as intrusion detection, smart homes and border protection.
Edit intent: clarity
Original:  In this paper, we present the design, implementation and evaluation of RASID, a DfP system for human motion detection.
Revised:  We present the design, implementation and evaluation of RASID, a DfP system for human motion detection.
Edit intent: coherence
Original:  RASID combines different modules for statistical anomaly detection while adapting to changes in the environment to provide accurate, robust  and low-overhead detection of human activities  .
Revised:  RASID combines different modules for statistical anomaly detection while adapting to changes in the environment to provide accurate, robust , and low-overhead detection of human activities .
Edit intent: fluency
Original:  Evaluation of the system in two different real testbed environments shows that it can achieve an accurate detection capability of 6\% miss detection rate and 9\% false alarm rate in both environments  .
Revised:  Evaluation of the system in two different testbeds shows that it can achieve an accurate detection capability of 6\% miss detection rate and 9\% false alarm rate in both environments .
Edit intent: clarity
Original:  Evaluation of the system in two different real testbed environments shows that it can achieve an accurate detection capability of 6\% miss detection rate and 9\% false alarm rate in both environments  .
Revised:  Evaluation of the system in two different real testbed environments shows that it can achieve an accurate detection capability in both environments .
Edit intent: clarity
Original:  AGR with the assumption partitions the complexities of problems more detailedly, and finds out some new evidences for the security of cryptosystems.
Revised:  AGR with the assumption partitions the complexities of problems more detailedly, and finds out some new evidence for the security of cryptosystems.
Edit intent: fluency
Original:  The workshop focuses on non-conventional implementations of bioinspired algorithms and its conceptual implications 
Revised:  The workshop focuses on non-conventional implementations of bioinspired algorithms and its conceptual implications .
Edit intent: fluency
Original: In this work, we have presented a simple analytical approximation scheme for  generic non-linear FBSDEs.
Revised: In this work, we have presented a simple analytical approximation scheme for the generic non-linear FBSDEs.
Edit intent: fluency
Original:  The method presented in this paper may be useful for various important problems which have prevented from being studied analytically so far.
Revised:  The method presented in this paper may be useful for various important problems which have prevented analytical treatment so far.
Edit intent: clarity
Original: In this work, we have presented a simple analytical approximation scheme for the generic non-linear FBSDEs.
Revised: In this work, we have presented a simple analytical approximation scheme for generic non-linear FBSDEs.
Edit intent: fluency
Original:  The method was found to render the original non-linear PDE into a series of standard parabolic linear PDEs.
Revised:  The method is found to render the original non-linear PDE into a series of standard parabolic linear PDEs.
Edit intent: fluency
Original:  Two simple examples were provided to demonstrate how the perturbation works and show its accuracy relative to the known numerical techniques.
Revised:  Two simple examples are provided to demonstrate how the perturbation works and show its accuracy relative to the known numerical techniques.
Edit intent: fluency
Original:  Two simple examples were provided to demonstrate how the perturbation works and show its accuracy relative to the known numerical techniques.
Revised:  Two simple examples were provided to demonstrate how the perturbation works and show its accuracy relative to known numerical techniques.
Edit intent: fluency
Original:  The method presented in this paper may be useful for various important problems which have prevented analytical treatment so far.
Revised:  The method presented in this paper may be useful for various important problems which have eluded analytical treatment so far.
Edit intent: clarity
Original: In this article, we re-introduce the so called "Arkaden-Faden-Lage" (AFL for short) representation of knots in 3 dimensional space introduced by Kurt Reidemeister in the 1930s and show how it can be used to develop efficient algorithms to compute some important topological knot structures.
Revised: In this article, we re-introduce the so called "Arkaden-Faden-Lage" (AFL for short) representation of knots in 3 dimensional space introduced by Kurt Reidemeister and show how it can be used to develop efficient algorithms to compute some important topological knot structures.
Edit intent: coherence
Original:  As opposed to preferential attachment, the optimization framework accurately describes large-scale Internet evolution , predicting new links in the Internet with a remarkable precision.
Revised:  As opposed to preferential attachment, the optimization framework accurately describes large-scale Internet evolution , predicting new links in them with a remarkable precision.
Edit intent: clarity
Original:  If new connections are established preferentially to more popular nodes in a network , then the network is scale-free.
Revised:  If new connections are made preferentially to more popular nodes in a network , then the network is scale-free.
Edit intent: clarity
Original:  If new connections are established preferentially to more popular nodes in a network , then the network is scale-free.
Revised:  If new connections are established preferentially to more popular nodes , then the network is scale-free.
Edit intent: clarity
Original:  Here we show that not only popularity but also similarity is a strong force shaping the network structure and dynamics.
Revised:  Here we show that popularity is just one dimension of attractiveness. Another dimension is similarity.
Edit intent: coherence
Original:  The framework admits a geometric interpretation, in which preferential attachment emerges from local optimization processes .
Revised:  The framework admits a geometric interpretation, in which popularity preference emerges from local optimization processes .
Edit intent: clarity
Original:  The framework admits a geometric interpretation, in which preferential attachment emerges from local optimization processes .
Revised:  The framework admits a geometric interpretation, in which preferential attachment emerges from local optimization .
Edit intent: clarity
Original:  We give a proof of the fact that, under this model, the mass of the mold will eventually converge to the shortest s_0-s_1 path of the network that the mold lies on, independently of the structure of the network or of the initial mass distribution.
Revised:  We give a proof of the fact that, under this model, the mass of the mold will eventually converge to the shortest s0-s1 path of the network that the mold lies on, independently of the structure of the network or of the initial mass distribution.
Edit intent: clarity
Original:  A mathematical model has been proposed by biologists to describe the feedback mechanism used by the Physarum Polycephalum slime mold to adapt its tubular channels while foraging two food sources s_0 and s_1.
Revised:  A mathematical model has been proposed by biologists to describe the feedback mechanism used by the slime mold to adapt its tubular channels while foraging two food sources s_0 and s_1.
Edit intent: clarity
Original:  We give a proof of the fact that, under this model, the mass of the mold will eventually converge to the shortest s0-s1 path of the network that the mold lies on, independently of the structure of the network or of the initial mass distribution.
Revised:  We give a proof of the fact that, under this model, the mass of the mold will eventually converge to the shortest s0 - s1 path of the network that the mold lies on, independently of the structure of the network or of the initial mass distribution.
Edit intent: fluency
Original: Based on the phosphorelay kinetics operative within BvgAS two component system we propose a mathematical model for signal transduction and differential gene regulation in {\it Bordetella pertussis}.
Revised: Based on the phosphorelay kinetics operative within BvgAS two component system we propose a mathematical framework for signal transduction and differential gene regulation in {\it Bordetella pertussis}.
Edit intent: clarity
Original:  The quasi-steady state analysis reveals a positive feedback and temperature induced molecular switch, leading to graded response and amplification in the output of BvgA.
Revised:  The quasi-steady state analysis reveals a positive feedback and temperature induced molecular switch, leading to amplification in the output of BvgA.
Edit intent: clarity
Original:  Accumulation of  large pool of BvgA thus results into differential regulation of the downstream genes, including the gene encoding toxin.
Revised:  Accumulation of a large pool of BvgA thus results into differential regulation of the downstream genes, including the gene encoding toxin.
Edit intent: fluency
Original:  The proposed model identifies a novel mechanism of transcriptional interference between two promoters present in the %DIFDELCMD < {\it %%% bvg locus.
Revised:  The proposed model identifies a novel mechanism of transcriptional interference between two promoters present in the %DIFDELCMD < {\it %%% bvg locus.
Edit intent: fluency
Original:   It's concluded that signi?cant evidence exists that P=NP.
Revised:  It's concluded that significant evidence exists that P=NP.
Edit intent: fluency
Original:  There is a forum devoted to this paper at URL All are in- vited to correspond here and help with the anal- ysis of the algorithm. 
Revised:  There is a forum devoted to this paper at URL All are invited to correspond here and help with the anal- ysis of the algorithm. 
Edit intent: fluency
Original:  There is a forum devoted to this paper at URL All are in- vited to correspond here and help with the anal- ysis of the algorithm. 
Revised:  There is a forum devoted to this paper at URL All are in- vited to correspond here and help with the analysis of the algorithm. 
Edit intent: fluency
Original: We show that for every compact convex set S in the plane and every 0 < \alpha < \pi, there exist a point O and two supporting lines to S passing through O and touching S at twosingle points X and Y, respectively, such that |OX|=|OY| and the angle between the two lines has measure \alpha.
Revised: single points X and Y, respectively, such that |OX|=|OY| and the angle between the two lines has measure \alpha.
Edit intent: coherence
Original: We show that for every compact convex set S in the plane and every 0 < \alpha < \pi, there exist a point O and two supporting lines to S passing through O and touching S at twosingle points X and Y, respectively, such that |OX|=|OY| and the angle between the two lines has measure \alpha.
Revised: We show that for every compact convex set S in the plane and every 0 < \alpha < \pi, there exist a point O and two supporting lines to S passing through O and touching S at two X and Y, respectively, such that |OX|=|OY| and the angle between the two lines has measure \alpha.
Edit intent: clarity
Original:  In addition, we also consider the log-%DIFDELCMD < \lev %DIFDELCMD < %%%  approximation of annuities, which offers good approximations for high volatility regimes.
Revised:  In addition, we also consider the %DIFDELCMD < \lev %DIFDELCMD < %%% approximation of annuities, which offers good approximations for high volatility regimes.
Edit intent: coherence
Original: We present a continuum model of the coupling between cells and substrate that accounts for some of the observed substrate-sti?ness dependence of cell properties.
Revised: We present a continuum model of the coupling between cells and substrate that accounts for some of the observed substrate-stiffness dependence of cell properties.
Edit intent: fluency
Original:  The cell is modeled as an elastic active gel, adapting recently developed continuum theories of active viscoleastic fluids.
Revised:  The cell is modeled as an elastic active gel, adapting recently developed continuum theories of active viscoelastic fluids.
Edit intent: fluency
Original:  The coupling to the substrate enters as a boundary condition that relates the cell's deformation ? field to local stress gradients.
Revised:  The coupling to the substrate enters as a boundary condition that relates the cell's deformation field to local stress gradients.
Edit intent: fluency
Original: In network tomography , we seek to infer the status of parameters ( such as delay) for  links inside a network through end-to-end probing between (external) boundary nodes along chosen routes.
Revised: One of the purposes of network tomography is to infer the status of parameters ( such as delay) for links inside a network through end-to-end probing between (external) boundary nodes along chosen routes.
Edit intent: clarity
Original: In network tomography , we seek to infer the status of parameters ( such as delay) for  links inside a network through end-to-end probing between (external) boundary nodes along chosen routes.
Revised: In network tomography , we seek to infer the status of parameters ( e.g., delay) for links inside a network through end-to-end probing between (external) boundary nodes along chosen routes.
Edit intent: clarity
Original: In network tomography , we seek to infer the status of parameters ( such as delay) for  links inside a network through end-to-end probing between (external) boundary nodes along chosen routes.
Revised: In network tomography , we seek to infer the status of parameters ( such as delay) for the links inside a network through end-to-end probing between (external) boundary nodes along chosen routes.
Edit intent: fluency