wanyu/IteraTeR_v2 huggingface dataset:
Original:  Due to this, we are able to capture the variation of modular organization across states , timescales, and in response to different perturbations, aspects of modularity which are all relevant to real-world dynamical systems.
Revised:  Due to this, we are able to capture the variation of modular organization across states , and in response to different perturbations, aspects of modularity which are all relevant to real-world dynamical systems.
Edit intent: clarity
Original:  Due to this, we are able to capture the variation of modular organization across states , timescales, and in response to different perturbations, aspects of modularity which are all relevant to real-world dynamical systems.
Revised:  Due to this, we are able to capture the variation of modular organization across states , timescales, and in response to different kinds of perturbations: aspects of modularity which are all relevant to real-world dynamical systems.
Edit intent: clarity
Original:  It uncovers hierarchical modular organization present in a system's coupling matrix.
Revised:  It uncovers hierarchical modular organization planted in a system's coupling matrix.
Edit intent: clarity
Original:  It also identifies the onset of a self-organized modular regime in coupled map lattices, where it is used to explore dependence of modularity on system state, parameters, and perturbations .
Revised:  It also identifies the onset of a self-organized modular regime in coupled map lattices, it identifies the presence of self-organized modularity that depends on the initial state, dynamical parameters, and perturbations .
Edit intent: clarity
Original:  It also identifies the onset of a self-organized modular regime in coupled map lattices, where it is used to explore dependence of modularity on system state, parameters, and perturbations .
Revised:  It also identifies the onset of a self-organized modular regime in coupled map lattices, where it is used to explore dependence of modularity on system state, parameters, and type of perturbations. Our approach offers a powerful tool for exploring the modular organization of complex dynamical systems .
Edit intent: clarity
Original:  On pristine (un-repeatmasked) mammalian whole-genome assemblies we perform a genome "intersection" that in general consumes less than a tenth of the computation time required by commonly used methods for genome alignment, and we extract "non-embedded maximal matches," maximal matches that are not embedded into other maximal matches, as potential orthologs.
Revised:  On pristine (un-repeatmasked) mammalian whole-genome assemblies we perform a genome "intersection" that in general consumes less than one thirtieth of the computation time required by commonly used methods for genome alignment, and we extract "non-embedded maximal matches," maximal matches that are not embedded into other maximal matches, as potential orthologs.
Edit intent: clarity
Original:  On pristine (un-repeatmasked) mammalian whole-genome assemblies we perform a genome "intersection" that in general consumes less than a tenth of the computation time required by commonly used methods for genome alignment, and we extract "non-embedded maximal matches," maximal matches that are not embedded into other maximal matches, as potential orthologs.
Revised:  On pristine (un-repeatmasked) mammalian whole-genome assemblies we perform a genome "intersection" that in general consumes less than a tenth of the computation time required by commonly used methods for whole-genome alignment, and we extract "non-embedded maximal matches," maximal matches that are not embedded into other maximal matches, as potential orthologs.
Edit intent: fluency
Original: This article proposes a convenient tool for decoding the output of neural networks trained by connectionist temporal classification (CTC) for handwritten text recognition.
Revised: This article proposes a convenient tool for decoding the output of neural networks trained by Connectionist Temporal Classification (CTC) for handwritten text recognition.
Edit intent: fluency
Original:  We use regular expressions to describe the complex structures we are expecting in the writing.
Revised:  We use regular expressions to describe the complex structures expected in the writing.
Edit intent: clarity
Original:  We refer to applications where we successfully integrated the proposed decoder  .
Revised:  We refer to applications where we integrated the proposed decoder .
Edit intent: clarity
Original: There are many constraints on population growth or decay in a country : several are of socio-economic origins.
Revised: Population growth (or decay) in a country : several are of socio-economic origins.
Edit intent: clarity
Original: There are many constraints on population growth or decay in a country : several are of socio-economic origins.
Revised: There are many constraints on population growth or decay in a country can be due to various f socio-economic origins.
Edit intent: clarity
Original:  In this paper it is proved that every cubic, vertex-transitive partial cube is isomorphic to one of the following graphs: K_2 \, \square \, C_{2n}, for some n\geq 2,  generalized Petersen graph G(10,3), permutahedron, truncated cuboctahedron, or  truncated icosidodecahedron.
Revised:  In this paper it is proved that every cubic, vertex-transitive partial cube is isomorphic to one of the following graphs: K_2 \, \square \, C_{2n}, for some n\geq 2, the generalized Petersen graph G(10,3), permutahedron, truncated cuboctahedron, or truncated icosidodecahedron.
Edit intent: clarity
Original:  In this paper it is proved that every cubic, vertex-transitive partial cube is isomorphic to one of the following graphs: K_2 \, \square \, C_{2n}, for some n\geq 2,  generalized Petersen graph G(10,3), permutahedron, truncated cuboctahedron, or  truncated icosidodecahedron.
Revised:  In this paper it is proved that every cubic, vertex-transitive partial cube is isomorphic to one of the following graphs: K_2 \, \square \, C_{2n}, for some n\geq 2, generalized Petersen graph G(10,3), the cubic permutahedron, the truncated cuboctahedron, or truncated icosidodecahedron.
Edit intent: clarity
Original:  In this paper it is proved that every cubic, vertex-transitive partial cube is isomorphic to one of the following graphs: K_2 \, \square \, C_{2n}, for some n\geq 2,  generalized Petersen graph G(10,3), permutahedron, truncated cuboctahedron, or  truncated icosidodecahedron.
Revised:  In this paper it is proved that every cubic, vertex-transitive partial cube is isomorphic to one of the following graphs: K_2 \, \square \, C_{2n}, for some n\geq 2, generalized Petersen graph G(10,3), permutahedron, truncated cuboctahedron, or the truncated icosidodecahedron.
Edit intent: clarity
Original:  This complete classification of cubic, vertex-transitive partial cubes, a family that includes all cubic, distance-regular partial cubes (Weichsel, 1992), is a generalization of results of Bresar et . al. from 2004 on cubic mirror graphs, and a contribution to the classification of all cubic partial cubes.
Revised:  This classification is a generalization of results of Bresar et . al. from 2004 on cubic mirror graphs, and a contribution to the classification of all cubic partial cubes.
Edit intent: clarity
Original:  This complete classification of cubic, vertex-transitive partial cubes, a family that includes all cubic, distance-regular partial cubes (Weichsel, 1992), is a generalization of results of Bresar et . al. from 2004 on cubic mirror graphs, and a contribution to the classification of all cubic partial cubes.
Revised:  This complete classification of cubic, vertex-transitive partial cubes, a family that includes all cubic, distance-regular partial cubes (Weichsel, 1992), is a generalization of results of Bresar et al.~ from 2004 on cubic mirror graphs, and a contribution to the classification of all cubic partial cubes.
Edit intent: fluency
Original:  This complete classification of cubic, vertex-transitive partial cubes, a family that includes all cubic, distance-regular partial cubes (Weichsel, 1992), is a generalization of results of Bresar et . al. from 2004 on cubic mirror graphs, and a contribution to the classification of all cubic partial cubes.
Revised:  This complete classification of cubic, vertex-transitive partial cubes, a family that includes all cubic, distance-regular partial cubes (Weichsel, 1992), is a generalization of results of Bresar et . al. from 2004 on cubic mirror graphs, it includes all cubic, distance-regular partial cubes (Weichsel, 1992), and presents a contribution to the classification of all cubic partial cubes.
Edit intent: coherence
Original:  The Tukey depth of a point q with respect to X is the minimum number \tau_X(q) of points of X in a halfspace containing q. In this paper we prove a depth version of Caratheodory 's theorem.
Revised:  The Tukey depth of a point q with respect to X is the minimum number \tau_X(q) of points of X in a halfspace containing q. In this paper we prove a depth version of Carath\'eodory 's theorem.
Edit intent: fluency
Original:  To store the information necessary for random access, we suggest 10 bytes per triangle and 14 bytes per tetrahedron.
Revised:  To store sufficient information for random access, we suggest 10 bytes per triangle and 14 bytes per tetrahedron.
Edit intent: clarity
Original: Community-detection methods that describe large-scale patterns in the dynamics on and of networks suffer from effects of limited memory and arbitrary time binning.
Revised: Methods for identification of dynamical patterns in networks suffer from effects of limited memory and arbitrary time binning.
Edit intent: clarity
Original:  Here we  develop a principled method to identify patterns on dynamics that take place on network systems, as well as on the dynamics that shape the network themselves, without requiring the stipulation of relevant time scales, which instead are determined solely from data.
Revised:  Here we develop a principled data-driven method that determines relevant timescales and identifies patterns of dynamics that take place on network systems, as well as on the dynamics that shape the network themselves, without requiring the stipulation of relevant time scales, which instead are determined solely from data.
Edit intent: clarity
Original:  Here we  develop a principled method to identify patterns on dynamics that take place on network systems, as well as on the dynamics that shape the network themselves, without requiring the stipulation of relevant time scales, which instead are determined solely from data.
Revised:  Here we develop a principled method to identify patterns on dynamics that take place on networks as well as on the dynamics that shape the network themselves, without requiring the stipulation of relevant time scales, which instead are determined solely from data.
Edit intent: clarity
Original:  Unfortunately, due to the computational bottleneck associated with optimizing L1-penalties, it is not practical to apply such methods to learn large-scale brain networks  .
Revised:  Unfortunately, due to the computational bottleneck associated with optimizing L1-penalties, it is not practical to apply such methods to construct large-scale brain networks .
Edit intent: clarity
Original:  In this paper, we introduce a new sparse network model based on cross-correlations that bypass the computational bottleneck.
Revised:  In this paper, we introduce a new sparse network model using cross-correlations that bypass the computational bottleneck.
Edit intent: coherence
Original:  Our model can build the sparse brain networks at  voxel level with p > 25000.
Revised:  Our model can build sparse brain networks at voxel level with p > 25000.
Edit intent: clarity
Original:  Our model can build the sparse brain networks at  voxel level with p > 25000.
Revised:  Our model can build the sparse brain networks at the voxel level with p > 25000.
Edit intent: fluency
Original:  The method is subsequently applied in determining the extend of genetic effects on functional brain networks at voxel-level for the first time using twin fMRI.
Revised:  The method is subsequently applied in determining the extent of heritability on a functional brain network at the voxel-level for the first time using twin fMRI.
Edit intent: clarity
Original: We introduce an improved model for human communication patterns, in particular for arrival times of Twitter tweets.
Revised: One of the popular research topics on networked humanity is to understand how people interact and communicate. Scholars investigated the arising communication patterns, in particular for arrival times of Twitter tweets.
Edit intent: clarity
Original:  The distribution of waiting times separating two consecutive events - also denoted by the inter-event distribution - is well known have a density fitting a power-law.
Revised:  While the distribution of inter-event distribution - is well known have a density fitting a power-law.
Edit intent: clarity
Original:  The first idea consists of separating the short waiting times - out of scope for power-law distributions - from the long ones.
Revised:  The first idea consists of separating the short waiting times -- out of scope for power-law distributions - from the long ones.
Edit intent: fluency
Original:  The first idea consists of separating the short waiting times - out of scope for power-law distributions - from the long ones.
Revised:  The first idea consists of separating the short waiting times - out of scope for power-law distributions -- from the long ones.
Edit intent: fluency
Original: It has long been conjectured that hypothesis spaces suitable for data that is compositional in nature, such as text or images, may be more efficiently represented with deep hierarchical architectures than with shallow ones.
Revised: It has long been conjectured that hypotheses spaces suitable for data that is compositional in nature, such as text or images, may be more efficiently represented with deep hierarchical architectures than with shallow ones.
Edit intent: fluency
Original: It has long been conjectured that hypothesis spaces suitable for data that is compositional in nature, such as text or images, may be more efficiently represented with deep hierarchical architectures than with shallow ones.
Revised: It has long been conjectured that hypothesis spaces suitable for data that is compositional in nature, such as text or images, may be more efficiently represented with deep hierarchical networks than with shallow ones.
Edit intent: clarity
Original:  Despite the vast empirical evidence , formal arguments to date are limited and do not capture the kind of networks used in practice.
Revised:  Despite the vast empirical evidence supporting this belief, theoretical justifications to date are limited and do not capture the kind of networks used in practice.
Edit intent: clarity
Original:  We show that a shallow network corresponds to a rank-1  decomposition, whereas a deep network corresponds to a Hierarchical Tucker (HT) decomposition.
Revised:  We show that a shallow network corresponds to a rank-1 ) decomposition, whereas a deep network corresponds to a Hierarchical Tucker (HT) decomposition.
Edit intent: fluency
Original:  In deep learning terminology, this amounts to saying that besides a negligible set, all functions that can be implemented by a deep network of polynomial size, require an exponential size if one wishes to implement (or approximate) them with a shallow network.
Revised:  In deep learning terminology, this amounts to saying that besides a negligible set, all functions that can be implemented by a deep network of polynomial size, require exponential size in order to be realized (or even approximated) by a shallow network.
Edit intent: clarity
Original:  Our construction and theory  shed new light on various practices and ideas employed by the deep learning community , and in that sense bear a paradigmatic contribution as well .
Revised:  Our construction and theory shed new light on various practices and ideas employed by the deep learning community .
Edit intent: coherence
Original:  With the massive growth of online social networks like Facebook, Twitter etc.  it has become a problem of extreme importance to know the destiny of these networks.
Revised:  With the massive growth of online social networks like Facebook, Twitter etc. So it has become a problem of extreme importance to know the destiny of these networks.
Edit intent: coherence
Original:  We model the social network as an undirected graph where nodes represent people and edges represent the friendship relation between them.
Revised:  We model the social network as an undirected graph where nodes represent people and edges represent the friendship between them.
Edit intent: clarity
Original:  We also discuss how our model can be used to model various complex social networks other than online social networks like political networks, various organizations etc  .
Revised:  We also discuss how our model can be used to model various complex social networks other than online social networks like political networks, various organizations etc . .
Edit intent: fluency
Original:  We show for most classification problems three layers are sufficient and the network size depends  the number of clusters.
Revised:  We show for most classification problems three layers are sufficient and the network size depends on the number of clusters.
Edit intent: clarity
Original:  It yields a new and shorter /simpler proof of the theorem of A. Aggarwal that \left\lfloor\frac{3 n +4}{16}\right\rfloor mobile guards are sufficient to control the interior of an n vertex orthogonal polygon.
Revised:  It yields a new and shorter proof of the theorem of A. Aggarwal that \left\lfloor\frac{3 n +4}{16}\right\rfloor mobile guards are sufficient to control the interior of an n vertex orthogonal polygon.
Edit intent: clarity
Original:  It yields a new and shorter /simpler proof of the theorem of A. Aggarwal that \left\lfloor\frac{3 n +4}{16}\right\rfloor mobile guards are sufficient to control the interior of an n vertex orthogonal polygon.
Revised:  It yields a new and shorter /simpler proof of the theorem of A. Aggarwal that \left\lfloor\frac{3 n +4}{16}\right\rfloor mobile guards are sufficient to control the interior of an n-vertex orthogonal polygon.
Edit intent: fluency
Original:  It is a further proof of the "metatheorem" that the (orthogonal) art gallery theorems are based on partition theorems.
Revised:  It is a further proof of the "metatheorem" that (orthogonal) art gallery theorems are based on partition theorems.
Edit intent: fluency
Original:  It yields a new and shorter proof of the theorem of A.  Aggarwal that \left\lfloor\frac{3 n +4}{16}\right\rfloor mobile guards are sufficient to control the interior of an n-vertex orthogonal polygon.
Revised:  It yields a new and shorter proof of the theorem of A. ~ Aggarwal that \left\lfloor\frac{3 n +4}{16}\right\rfloor mobile guards are sufficient to control the interior of an n-vertex orthogonal polygon.
Edit intent: fluency
Original:  Our result is also a further proof of the "metatheorem" that (orthogonal) art gallery theorems are based on partition theorems.
Revised:  Our result is also a further example of the "metatheorem" that (orthogonal) art gallery theorems are based on partition theorems.
Edit intent: clarity
Original:  It yields a new and shorter proof of the theorem of A. ~ Aggarwal that \left\lfloor\frac{3 n +4}{16}\right\rfloor mobile guards are sufficient to control the interior of an n-vertex orthogonal polygon.
Revised:  It yields a new and shorter proof of the theorem of A. Aggarwal that \left\lfloor\frac{3 n +4}{16}\right\rfloor mobile guards are sufficient to control the interior of an n-vertex orthogonal polygon.
Edit intent: fluency
Original: \mathrm{V} \mathrm{V} We show that the word problem for omega-terms over each level of the Trotter-Weil Hierarchy is decidable ;
Revised: \mathrm{V} \mathrm{V}. We show that the word problem for omega-terms over each level of the Trotter-Weil Hierarchy is decidable ;
Edit intent: fluency
Original: \mathrm{V} \mathrm{V} We show that the word problem for omega-terms over each level of the Trotter-Weil Hierarchy is decidable ;
Revised: \mathrm{V} \mathrm{V} We show that the word problem for \omega-terms over each level of the Trotter-Weil Hierarchy is decidable ;
Edit intent: fluency
Original:  this means, for every variety V of the hierarchy and every identity u=v of omega-terms, one can decide whether all monoids in V satisfy u=v . More precisely, for every fixed variety V, the problem is solvable in nondeterministic logarithmic space (NL).
Revised:  this means, for every variety V of the hierarchy and every identity u=v of omega-terms, one can decide whether all monoids in V satisfy u=v . More precisely, for every fixed variety in the Trotter-Weil Hierarchy, our approach yields an algorithm in nondeterministic logarithmic space (NL).
Edit intent: clarity
Original:  In addition, we give deterministic polynomial time algorithms which are more efficient than straightforward translations of the NL-algorithms.
Revised:  In addition, we provide deterministic polynomial time algorithms which are more efficient than straightforward translations of the NL-algorithms.
Edit intent: fluency
Original:  From a language perspective, the word problem for omega-terms is the following: For every language variety V in the Trotter-Weil Hierarchy and every language variety W given by an identity of omega-terms, one can decide whether V is contained in W. This includes the case where V is some level of the FO2 quantifier alternation hierarchy.
Edit intent: coherence
Original:  As an application of our results, we show that the separation problems for the so-called  corners of the Trotter-Weil Hierarchy are decidable.
Revised:  As an application of our results, we show that separability by the so-called corners of the Trotter-Weil Hierarchy are decidable.
Edit intent: clarity
Original:  As an application of our results, we show that the separation problems for the so-called  corners of the Trotter-Weil Hierarchy are decidable.
Revised:  As an application of our results, we show that the separation problems for the so-called corners of the Trotter-Weil Hierarchy is decidable.
Edit intent: fluency
Original:  In this paper we survey some of the confusion about the meaning of CAP, including inconsistencies and ambiguities in its definitions, and we highlight some problems in its formalization and proofs . CAP is often interpreted as proof that eventually consistent databases have better availability properties than strongly consistent databases;
Revised:  In this paper we survey some of the confusion about the meaning of CAP, including inconsistencies and ambiguities in its definitions, and we highlight some problems in its formalization . CAP is often interpreted as proof that eventually consistent databases have better availability properties than strongly consistent databases;
Edit intent: clarity
Original:  Let in addition a mapping f on E be given that associate information with the edges (e.g., a pointer), such that f(e)=f(e') means that edges e and e' carry the same information;
Revised:  Let in addition a mapping f on E be given that associates information with the edges (e.g., a pointer), such that f(e)=f(e') means that edges e and e' carry the same information;
Edit intent: fluency
Original:  Unlike the  one every two nodes  downsampling operation on bipartite graphs, this coarsening operation does not have an exact formulation in the Fourier space of the graph.
Revised:  Unlike the " one every two nodes downsampling operation on bipartite graphs, this coarsening operation does not have an exact formulation in the Fourier space of the graph.
Edit intent: fluency
Original:  Unlike the  one every two nodes  downsampling operation on bipartite graphs, this coarsening operation does not have an exact formulation in the Fourier space of the graph.
Revised:  Unlike the one every two nodes " downsampling operation on bipartite graphs, this coarsening operation does not have an exact formulation in the Fourier space of the graph.
Edit intent: fluency