wanyu/IteraTeR_v2 huggingface dataset:
Original:  A by-product of our proof is a precise coupling-result for local-neighbourhoods in Degree-Corrected Planted-Partition models, which could be of independent interest ]  .
Revised:  As by-products of our proof is a precise coupling-result for local-neighbourhoods in Degree-Corrected Planted-Partition models, which could be of independent interest ] .
Edit intent: fluency
Original: Real-world networks, like social networks or the internet infrastructure, have structural properties such as their large clustering coefficient that can best be described in terms of an underlying geometry.
Revised: Real-world networks, like social networks or the internet infrastructure, have structural properties such as large clustering coefficients that can best be described in terms of an underlying geometry.
Edit intent: clarity
Original:  However, we do not directly study hyperbolic random graphs, but replace them by a more general model that we call geometric inhomogeneous random graphs (GIRGs).
Revised:  Instead of studying directly hyperbolic random graphs, but replace them by a more general model that we call geometric inhomogeneous random graphs (GIRGs).
Edit intent: coherence
Original:  However, we do not directly study hyperbolic random graphs, but replace them by a more general model that we call geometric inhomogeneous random graphs (GIRGs).
Revised:  However, we do not directly study hyperbolic random graphs, we use a generalization that we call geometric inhomogeneous random graphs (GIRGs).
Edit intent: clarity
Original:  However, we do not directly study hyperbolic random graphs, but replace them by a more general model that we call geometric inhomogeneous random graphs (GIRGs).
Revised:  However, we do not directly study hyperbolic random graphs, but replace them by a more general model that we call geometric inhomogeneous random graphs (GIRGs).
Edit intent: fluency
Original:  Since we ignore constant factors in the edge probabilities, our model is technically simpler (specifically, we avoid hyperbolic cosines), while preserving the qualitative behaviour of hyperbolic random graphs, and we suggest to replace hyperbolic random graphs by our new model in future theoretical studies.
Revised:  Since we ignore constant factors in the edge probabilities, our model is technically simpler (specifically, we avoid hyperbolic cosines), while preserving the qualitative behaviour of hyperbolic random graphs, and we suggest to replace hyperbolic random graphs by this new model in future theoretical studies.
Edit intent: clarity
Original:  we establish that GIRGs have a constant clustering coefficient } , (3) we show that GIRGs have small separators, i.e., it suffices to delete a sublinear number of edges to break the giant component into two large pieces, and (4) we show how to compress GIRGs using an expected linear number of bits.
Revised:  We establish that GIRGs have a constant clustering coefficient } , (3) we show that GIRGs have small separators, i.e., it suffices to delete a sublinear number of edges to break the giant component into two large pieces, and (4) we show how to compress GIRGs using an expected linear number of bits.
Edit intent: fluency
Original:  we establish that GIRGs have a constant clustering coefficient } , (3) we show that GIRGs have small separators, i.e., it suffices to delete a sublinear number of edges to break the giant component into two large pieces, and (4) we show how to compress GIRGs using an expected linear number of bits.
Revised:  we establish that GIRGs have clustering coefficients in } , (3) we show that GIRGs have small separators, i.e., it suffices to delete a sublinear number of edges to break the giant component into two large pieces, and (4) we show how to compress GIRGs using an expected linear number of bits.
Edit intent: clarity
Original:  we establish that GIRGs have a constant clustering coefficient } , (3) we show that GIRGs have small separators, i.e., it suffices to delete a sublinear number of edges to break the giant component into two large pieces, and (4) we show how to compress GIRGs using an expected linear number of bits.
Revised:  we establish that GIRGs have a constant clustering coefficient } , (3) we prove that GIRGs have small separators, i.e., it suffices to delete a sublinear number of edges to break the giant component into two large pieces, and (4) we show how to compress GIRGs using an expected linear number of bits.
Edit intent: coherence
Original: We present a flow-based network analysis of the directed connectome of the nematode Caenorhabditis elegans.
Revised: We exploit flow propagation on the directed neuronal network of the nematode Caenorhabditis elegans.
Edit intent: clarity
Original:  First, we use Directed Markov Stability community detection to find flow-retaining groupings of neurons at different levels of granularity, which are then related to functional and anatomical features.
Revised:  First, we use Directed Markov Stability community detection to find flow-retaining groupings of neurons at different levels of granularity, which we relate to functional and anatomical features.
Edit intent: coherence
Original:  We then carry out a systematic in silico evaluation of the full set of single and double ablations in the network, in order to identify node deletions that induce the most severe disruptions to the multi-resolution community structure.
Revised:  We then carry out a systematic in silico evaluation of the full set of single and double neuron ablations is used to identify deletions that induce the most severe disruptions to the multi-resolution community structure.
Edit intent: clarity
Original:  We then carry out a systematic in silico evaluation of the full set of single and double ablations in the network, in order to identify node deletions that induce the most severe disruptions to the multi-resolution community structure.
Revised:  We then carry out a systematic in silico evaluation of the full set of single and double ablations in the network, in order to identify node deletions that induce the most severe disruptions of the multi-resolution community structure.
Edit intent: fluency
Original:  We then carry out a systematic in silico evaluation of the full set of single and double ablations in the network, in order to identify node deletions that induce the most severe disruptions to the multi-resolution community structure.
Revised:  We then carry out a systematic in silico evaluation of the full set of single and double ablations in the network, in order to identify node deletions that induce the most severe disruptions to the multi-resolution flow structure.
Edit intent: clarity
Original:  Such ablations are shown to be linked to functionally relevant neurons  and suggest potential candidates for further in vivo investigation.
Revised:  Such ablations are linked to functionally relevant neurons and suggest potential candidates for further in vivo investigation.
Edit intent: clarity
Original:  Such ablations are shown to be linked to functionally relevant neurons  and suggest potential candidates for further in vivo investigation.
Revised:  Such ablations are shown to be linked to functionally relevant neurons , and suggest potential candidates for further in vivo investigation.
Edit intent: fluency
Original:  Second , we use the Role Based Similarity framework to identify four flow roles for the neurons in the connectome, based on the pattern of incoming and outgoing network flows for each node and without pre-imposing an a priori classification.
Revised:  In addition , we use the Role Based Similarity framework to identify four flow roles for the neurons in the connectome, based on the pattern of incoming and outgoing network flows for each node and without pre-imposing an a priori classification.
Edit intent: coherence
Original:  Second , we use the Role Based Similarity framework to identify four flow roles for the neurons in the connectome, based on the pattern of incoming and outgoing network flows for each node and without pre-imposing an a priori classification.
Revised:  Second , we use the Role Based Similarity framework to identify four roles for the neurons in the connectome, based on the pattern of incoming and outgoing network flows for each node and without pre-imposing an a priori classification.
Edit intent: clarity
Original:  Second , we use the Role Based Similarity framework to identify four flow roles for the neurons in the connectome, based on the pattern of incoming and outgoing network flows for each node and without pre-imposing an a priori classification.
Revised:  Second , we use the Role Based Similarity framework to identify four flow roles for the neurons in the connectome, without pre-imposing an a priori classification.
Edit intent: clarity
Original:  The flow roles identified are related to neuronal classifications and functionally important neuronal circuits , and interpreted in the light of signal propagation from biologically motivated inputs .
Revised:  The flow roles identified are related to neuronal classifications and functionally important neuronal circuits , and interpreted in the light of signal propagation motivated by biological input-response scenarios .
Edit intent: clarity
Original:  We find flow-retaining groupings of neurons at different levels of granularity, which we relate to functional and anatomical constituents of its nervous system.
Revised:  We find flow-based groupings of neurons at different levels of granularity, which we relate to functional and anatomical constituents of its nervous system.
Edit intent: clarity
Original:  In addition, we use the directional patterns of incoming and outgoing network flows at all scales to identify four roles for the neurons in the connectome, without pre-imposing a priori categories.
Revised:  In addition, we use the directional patterns of incoming and outgoing network flows at all scales to identify flow profiles for the neurons in the connectome, without pre-imposing a priori categories.
Edit intent: clarity
Original:  The identified roles are then linked to functional neuronal circuits in the context of signal propagation motivated by biological input-response scenarios.
Revised:  The four flow roles identified are linked to signal propagation motivated by biological input-response scenarios.
Edit intent: clarity
Original: Classification is a fundamental task in machine learning and artificial intelligence . Existing classification methods are designed to classify unknown instances within a set of previously known classes that are seen in training .
Revised: Classification is a fundamental task in machine learning and data mining . Existing classification methods are designed to classify unknown instances within a set of previously known classes that are seen in training .
Edit intent: clarity
Original:  Such classification takes the form of  prediction within a closed-set  . However, a more realistic scenario that fits the ground truth of real world applications is to consider the possibility of encountering instances that do not belong to any of the classes that are seen in training , i.e., an open-set classification.
Revised:  Such classification takes the form of a prediction within a closed-set . However, a more realistic scenario that fits the ground truth of real world applications is to consider the possibility of encountering instances that do not belong to any of the classes that are seen in training , i.e., an open-set classification.
Edit intent: fluency
Original:  Such classification takes the form of  prediction within a closed-set  . However, a more realistic scenario that fits the ground truth of real world applications is to consider the possibility of encountering instances that do not belong to any of the classes that are seen in training , i.e., an open-set classification.
Revised:  Such classification takes the form of prediction within a closed-set of classes . However, a more realistic scenario that fits the ground truth of real world applications is to consider the possibility of encountering instances that do not belong to any of the classes that are seen in training , i.e., an open-set classification.
Edit intent: clarity
Original:  Such classification takes the form of  prediction within a closed-set  . However, a more realistic scenario that fits the ground truth of real world applications is to consider the possibility of encountering instances that do not belong to any of the classes that are seen in training , i.e., an open-set classification.
Revised:  Such classification takes the form of prediction within a closed-set . However, a more realistic scenario that fits real-world applications is to consider the possibility of encountering instances that do not belong to any of the classes that are seen in training , i.e., an open-set classification.
Edit intent: clarity
Original:  Such classification takes the form of  prediction within a closed-set  . However, a more realistic scenario that fits the ground truth of real world applications is to consider the possibility of encountering instances that do not belong to any of the classes that are seen in training , i.e., an open-set classification.
Revised:  Such classification takes the form of prediction within a closed-set . However, a more realistic scenario that fits the ground truth of real world applications is to consider the possibility of encountering instances that do not belong to any of the training classes , i.e., an open-set classification.
Edit intent: clarity
Original:  In such situation, existing closed-set classification methods will assign a training label to these instances resulting in a misclassification.
Revised:  In such situation, existing closed-set classifiers will assign a training label to these instances resulting in a misclassification.
Edit intent: clarity
Original:  In this paper, we introduce Galaxy-X, a novel multi-class classification method for open-set problem .
Revised:  In this paper, we introduce Galaxy-X, a novel multi-class classification approach for open-set problem .
Edit intent: clarity
Original:  In such manner, our method is able to distinguish instances resembling previously seen classes from those that are of unseen classes .
Revised:  In such manner, our method is able to distinguish instances resembling previously seen classes from those that are of unknown ones .
Edit intent: clarity
Original:  Experimental results on benchmark datasets as well as on synthetic datasets show the efficiency of our approach in classifying novel instances from known as well as unknown classes.
Revised:  Experimental results on benchmark datasets show the efficiency of our approach in classifying novel instances from known as well as unknown classes.
Edit intent: clarity
Original:  Given an unannotated protein structure and a set of annotated proteins, ProtNN finds the nearest neighbor annotated structures based on protein graph pairwise similarities . ProtNN assigns to the query protein the function with the highest number of votes across the set of k nearest neighbor reference proteins, where k is a user defined parameter.
Revised:  Given an unannotated protein structure and a set of annotated proteins, ProtNN finds the nearest neighbor annotated structures based on protein graph pairwise similarities . ProtNN assigns to the query protein the function with the highest number of votes across the set of k nearest neighbor reference proteins, where k is a user-defined parameter.
Edit intent: fluency
Original: =u^{(m)}(x,1) \quad for \ \ x\in \Omega array\right. eqnarray* for some functions f,g, a drift a and a diffusion matrix A and \Omega\subset \mathbb R^n. Study of this model requires a simultaneous analysis of the differential equation and the recurrence relation.
Revised: =u^{(m)}(x,1) \quad for \ \ x\in \Omega array\right. eqnarray* for functions f,g, a drift a and a diffusion matrix A and \Omega\subset \mathbb R^n. Study of this model requires a simultaneous analysis of the differential equation and the recurrence relation.
Edit intent: clarity
Original:  When boundary conditions are hostile we provide critical domain results showing how extinction versus persistence of  species arises, depending on the size and geometry of the domain.
Revised:  When boundary conditions are hostile we provide critical domain results showing how extinction versus persistence of the species arises, depending on the size and geometry of the domain.
Edit intent: fluency
Original:  We show that there exists an {\it extreme volume size} such that for |\Omega| falls below this size the species is driven extinct, regardless of the geometry of the domain.
Revised:  We show that there exists an {\it extreme volume size} such that if |\Omega| falls below this size the species is driven extinct, regardless of the geometry of the domain.
Edit intent: fluency
Original:  For a given European option, an interval of rational pricesexists under a more general condition than the usual no-arbitrage requirement.
Revised:  For a given option, there exists an interval bounding the set of possible fair prices; such interval exists under more general conditions than the usual no-arbitrage requirement.
Edit intent: clarity
Original:  The paper develops computational results in order to evaluate the option bounds;
Revised:  The paper develops a backward recursive method to evaluate the option bounds;
Edit intent: clarity
Original:  A general class of trajectory sets is described for which the market model introduced by Britten Jones and Neuberger is nested as a particular case.
Revised:  Trajectory sets are introduced for which existing non-probabilistic markets models are nested as a particular case.
Edit intent: clarity
Original:  in R^{d} has the property that the convex hulls of all k-sets have a common transversal (d-\lambda)-plane. %DIFDELCMD < \smallskip\parIt %DIFDELCMD < %%%  turns out that m(k, d,\lambda) is strongly connected with other interesting problems, for instance, the chromatic number of Kneser hypergraphs and a discrete version of Rado's central Theorem.
Revised:  in R^{d} has the property that the convex hulls of all k-sets have a common transversal (d-\lambda)-plane. %DIFDELCMD < \smallskip\parIt %DIFDELCMD < %%% It turns out that m(k, d,\lambda) is strongly connected with other interesting problems, for instance, the chromatic number of Kneser hypergraphs and a discrete version of Rado's central Theorem.
Edit intent: fluency
Original: %DIFDELCMD < \par %%%  In the same spirit, we introduce a natural discrete version m^* of m by considering the existence of complete Kneser transversals .
Revised: %DIFDELCMD < \par %%% In the same spirit, we introduce a natural discrete version m^* of m by considering the existence of complete Kneser transversals .
Edit intent: fluency
Original:  By studying the so-called alternating oriented matroid we provide the asymptotic behavior of the function m^* for the family of cyclic polytopes.
Revised:  By studying the so-called alternating oriented matroid we provide the asymptotic behavior of the function m^* for the family of cyclic polytopes.
Edit intent: fluency
Original:  In 2010, the following function was introduced: m(k,d,\lambda) %DIFDELCMD < \mathrm{def}{=} %DIFDELCMD < %%%  the maximum positive integer n such that every set of n points (not necessarily in general position) in R^{d} has the property that the convex hulls of all k-sets have a common transversal (d-\lambda)-plane.
Revised:  Let m(k,d,\lambda) %DIFDELCMD < \mathrm{def}{=} %DIFDELCMD < %%% the maximum positive integer n such that every set of n points (not necessarily in general position) in R^{d} has the property that the convex hulls of all k-sets have a common transversal (d-\lambda)-plane.
Edit intent: coherence
Original:  By studying the so-called alternating oriented matroid we provide the asymptotic behavior of the function m^* for the family of cyclic polytopes.
Revised:  By studying the alternating oriented matroid we provide the asymptotic behavior of the function m^* for the family of cyclic polytopes.
Edit intent: clarity
Original:  By studying the so-called alternating oriented matroid we provide the asymptotic behavior of the function m^* for the family of cyclic polytopes.
Revised:  By studying the so-called alternating oriented matroid we obtain the asymptotic behavior of the function m^* for the family of cyclic polytopes.
Edit intent: clarity
Original:  Here we propose a hybrid modeling scheme combining the efficiency of  simplified point-neuron network models with the biophysical principles underlying LFP generation by real neurons.
Revised:  Here we propose a hybrid modeling scheme combining the efficiency of commonly used simplified point-neuron network models with the biophysical principles underlying LFP generation by real neurons.
Edit intent: clarity
Original:  We apply the scheme to a full-scale cortical network model for a ~1 \sim1 mm^2 patch of primary visual cortex and predict laminar LFPs for different network states, assess the relative LFP contribution from different laminar populations, and investigate the role of synaptic input correlations and neuron density on the LFP   .
Revised:  We apply the scheme to a full-scale cortical network model for a \sim1 mm^2 patch of primary visual cortex and predict laminar LFPs for different network states, assess the relative LFP contribution from different laminar populations, and investigate the role of synaptic input correlations and neuron density on the LFP .
Edit intent: clarity
Original: For a connected labelled graph G, a {\em spanning tree} T is a connected and an acyclic subgraph that spans all the vertices of G. In this paper, we consider a classical combinatorial problem which is to list all spanning trees of G. A Halin graph is a graph obtained from a tree with no degree two vertices and by joining all leaves with a cycle.
Revised: For a connected labelled graph G, a {\em spanning tree} T is a connected and an acyclic subgraph that spans all vertices of G. In this paper, we consider a classical combinatorial problem which is to list all spanning trees of G. A Halin graph is a graph obtained from a tree with no degree two vertices and by joining all leaves with a cycle.
Edit intent: fluency
Original: We consider the problem of low rank approximation of binary matrices .
Revised: We consider the problem of low rank approximation of binary matrix .
Edit intent: fluency
Original:  Here we are given a d \times n binary matrix A and a small integer k < d . The goal is to find two binary matrices U and V of sizes d \times k and k \times n respectively, so that the Frobenius norm of A-U V is minimized.
Revised:  Here we are given a d \times n binary matrix A and a small integer k . The goal is to find two binary matrices U and V of sizes d \times k and k \times n respectively, so that the Frobenius norm of A-U V is minimized.
Edit intent: clarity
Original:  Here we are given a d \times n binary matrix A and a small integer k < d . The goal is to find two binary matrices U and V of sizes d \times k and k \times n respectively, so that the Frobenius norm of A-U V is minimized.
Revised:  Here we are given a d \times n binary matrix A and a small integer k < d . The goal is to find two binary matrices U and V of sizes d \times k and k \times n respectively, so that the Frobenius norm of A - U V is minimized.
Edit intent: clarity
Original:  There are two models of this problem, depending on the definition of the  product of binary matrices : The GF(2) model and the Boolean semiring model.
Revised:  There are two models of this problem, depending on the definition of the product of binary vectors : The GF(2) model and the Boolean semiring model.
Edit intent: clarity
Original:  Previously, the only known results are 2-approximation algorithms for the special case k= 1 \mbox{ KDD:ShenJY09, Jiang14 In this paper, we give the first results for the general case k >1 for both GF(2) and Boolean model.
Revised:  Previously, the only known results are 2-approximation algorithms for the special case k= 1. In this paper, we give the first results for the general case k >1 for both GF(2) and Boolean model.
Edit intent: coherence