wanyu/IteraTeR_v2 huggingface dataset:
Original: The stochastic block model (SBM) is a popular tool for community detection in networks, but fitting it by maximum likelihood (MLE) involves an infeasible optimization problem.
Revised: The stochastic block model (SBM) is a popular tool for community detection in networks, but fitting it by maximum likelihood (MLE) involves a computationally infeasible optimization problem.
Edit intent: clarity
Original:  We propose a new semi-definite programming (SDP) solution to the problem of fitting the SBM, derived as a relaxation of the MLE.
Revised:  We propose a new semidefinite programming (SDP) solution to the problem of fitting the SBM, derived as a relaxation of the MLE.
Edit intent: fluency
Original:  Our relaxation, which we call SDP-1, is tighter than other recently proposed SDP relaxations, namely what we call SDP-2 and SDP-3, and thus previously established theoretical guarantees carry over.
Revised:  Our relaxation, which we call SDP-1, is tighter than other recently proposed SDP relaxations, and thus previously established theoretical guarantees carry over.
Edit intent: coherence
Original:  However, we show that SDP-1 is, in fact, strongly consistent (i.e., exactly recovers true communities ) over a wider class of SBMs than what current resultssuggest .
Revised:  However, we show that SDP-1 exactly recovers true communities ) over a wider class of SBMs than what current resultssuggest .
Edit intent: coherence
Original:  However, we show that SDP-1 is, in fact, strongly consistent (i.e., exactly recovers true communities ) over a wider class of SBMs than what current resultssuggest .
Revised:  However, we show that SDP-1 is, in fact, strongly consistent (i.e., exactly recovers true communities over a wider class of SBMs than what current resultssuggest .
Edit intent: fluency
Original:  However, we show that SDP-1 is, in fact, strongly consistent (i.e., exactly recovers true communities ) over a wider class of SBMs than what current resultssuggest .
Revised:  However, we show that SDP-1 is, in fact, strongly consistent (i.e., exactly recovers true communities ) over a wider class of SBMs than those covered by current results .
Edit intent: clarity
Original:  In particular, one can relax the assumption of strong assortativity  , implicit in consistency conditions of current SDPs, to that of (weak ) assortativity for SDP-1, thus , significantly broadening the class of applicable models.
Revised:  In particular, the assumption of strong assortativity , implicit in consistency conditions of current SDPs, to that of (weak ) assortativity for SDP-1, thus , significantly broadening the class of applicable models.
Edit intent: clarity
Original:  Another feature of our relaxation is the tendency to produce more balanced (i.e., equal-sized) communities which, as we show with a real-data example, makes it the ideal tool for fitting network histograms, a concept gaining popularity in the graphon estimation literature .
Revised:  Another feature of our relaxation is the tendency to produce communities of similar sizes. This tendency makes it the ideal tool for fitting network histograms, a concept gaining popularity in the graphon estimation literature .
Edit intent: clarity
Original:  Another feature of our relaxation is the tendency to produce more balanced (i.e., equal-sized) communities which, as we show with a real-data example, makes it the ideal tool for fitting network histograms, a concept gaining popularity in the graphon estimation literature .
Revised:  Another feature of our relaxation is the tendency to produce more balanced (i.e., equal-sized) communities which, as we show with a real-data example, makes it the ideal tool for fitting network histograms, a method gaining popularity in the graphon estimation literature .
Edit intent: clarity
Original: We give a brief application of mesoscopic response functions (MRFs) to  a large set of networks of fungi and slime moulds  .
Revised: We investigate the application of mesoscopic response functions (MRFs) to a large set of networks of fungi and slime moulds .
Edit intent: clarity
Original: We give a brief application of mesoscopic response functions (MRFs) to  a large set of networks of fungi and slime moulds  .
Revised: We give a brief application of mesoscopic response functions (MRFs) to characterise a large set of networks of fungi and slime moulds .
Edit intent: clarity
Original:  We construct "structural networks" by estimating cord conductances (which yield edge weights) from experimental data and "functional networks" by calculating edge weights based on how much nutrient traffic is predicted to occur on each edge.
Revised:  We construct "structural networks" by estimating cord conductances (which yield edge weights) from the experimental data, and we construct "functional networks" by calculating edge weights based on how much nutrient traffic is predicted to occur on each edge.
Edit intent: coherence
Original: We investigate the application of mesoscopic response functions (MRFs) to characterise a large set of networks of fungi and slime moulds grown under a wide variety of different experimental treatments, including inter-species competition and attack by fungivores.
Revised: We investigate the application of mesoscopic response functions (MRFs) to characterize a large set of networks of fungi and slime moulds grown under a wide variety of different experimental treatments, including inter-species competition and attack by fungivores.
Edit intent: fluency
Original:  We construct "structural networks" by estimating cord conductances (which yield edge weights) from the experimental data, and we construct "functional networks" by calculating edge weights based on how much nutrient traffic is predicted to occur on each edge.
Revised:  We construct 'structural networks' by estimating cord conductances (which yield edge weights) from the experimental data, and we construct "functional networks" by calculating edge weights based on how much nutrient traffic is predicted to occur on each edge.
Edit intent: fluency
Original:  We construct "structural networks" by estimating cord conductances (which yield edge weights) from the experimental data, and we construct "functional networks" by calculating edge weights based on how much nutrient traffic is predicted to occur on each edge.
Revised:  We construct "structural networks" by estimating cord conductances (which yield edge weights) from the experimental data, and we construct 'functional networks' by calculating edge weights based on how much nutrient traffic is predicted to occur on each edge.
Edit intent: fluency
Original:  We construct "structural networks" by estimating cord conductances (which yield edge weights) from the experimental data, and we construct "functional networks" by calculating edge weights based on how much nutrient traffic is predicted to occur on each edge.
Revised:  We construct "structural networks" by estimating cord conductances (which yield edge weights) from the experimental data, and we construct "functional networks" by calculating edge weights based on how much nutrient traffic is predicted to occur along each edge.
Edit intent: fluency
Original:  Both types of networks have the same topology, and we compute MRFs for both families of networks to illustrate two different ways of constructing taxonomies to group the biological networks into related clusters .
Revised:  Both types of networks have the same topology, and we compute MRFs for both families of networks to illustrate two different ways of constructing taxonomies to group the networks into clusters of related fungi and slime moulds .
Edit intent: clarity
Original:  Although both network taxonomies generate intuitively sensible groupings of networks across species, treatments , and laboratories, we find that clustering using the functional-network measure appears to give groups with lower intra-group variation in species or treatments.
Revised:  Although both network taxonomies generate intuitively sensible groupings of networks across species, treatments and laboratories, we find that clustering using the functional-network measure appears to give groups with lower intra-group variation in species or treatments.
Edit intent: fluency
Original:  We argue that MRFs provide a useful quantitative measures of network behaviour that can (1) help summarize an expanding set of increasingly complex experimental biological networks and (2) help extract information that captures subtle changes in intra-specific and inter-specific phenotypic traits that are integral to a mechanistic understanding of fungal behaviour and ecology.
Revised:  We argue that MRFs provide a useful quantitative analysis of network behaviour that can (1) help summarize an expanding set of increasingly complex experimental biological networks and (2) help extract information that captures subtle changes in intra-specific and inter-specific phenotypic traits that are integral to a mechanistic understanding of fungal behaviour and ecology.
Edit intent: clarity
Original:  We argue that MRFs provide a useful quantitative measures of network behaviour that can (1) help summarize an expanding set of increasingly complex experimental biological networks and (2) help extract information that captures subtle changes in intra-specific and inter-specific phenotypic traits that are integral to a mechanistic understanding of fungal behaviour and ecology.
Revised:  We argue that MRFs provide a useful quantitative measures of network behaviour that can (1) help summarize an expanding set of increasingly complex biological networks and (2) help extract information that captures subtle changes in intra-specific and inter-specific phenotypic traits that are integral to a mechanistic understanding of fungal behaviour and ecology.
Edit intent: clarity
Original:  We argue that MRFs provide a useful quantitative measures of network behaviour that can (1) help summarize an expanding set of increasingly complex experimental biological networks and (2) help extract information that captures subtle changes in intra-specific and inter-specific phenotypic traits that are integral to a mechanistic understanding of fungal behaviour and ecology.
Revised:  We argue that MRFs provide a useful quantitative measures of network behaviour that can (1) help summarize an expanding set of increasingly complex experimental biological networks and (2) help extract information that captures subtle changes in intra- and inter-specific phenotypic traits that are integral to a mechanistic understanding of fungal behaviour and ecology.
Edit intent: fluency
Original:  This communication scheme, examining relay cooperationfrom the physical layer perspective, has up to now yielded well-known results.
Revised:  Work on relay cooperation, from a physical layer perspective, has up to now yielded well-known results.
Edit intent: clarity
Original:  This paper takes a different stance focusing on the network-level cooperation.
Revised:  This paper takes a different stance focusing on network-level cooperation.
Edit intent: fluency
Original:  Extending previous results for a single relay, here we investigate the benefits from the deployment of a second one.
Revised:  Extending previous results for a single relay, we investigate here the benefits from the deployment of a second one.
Edit intent: fluency
Original:  We assume that the two relays do not generate packets of their own , the users have saturated queues and that the communication employs random access to the medium with slotted time .
Revised:  We assume that the two relays do not generate packets of their own and the system employs random access to the medium with slotted time .
Edit intent: clarity
Original:  We obtain analytical expressions for the arrival and service rates of the queues of the two relays and the stability conditions , under the collision channel .
Revised:  We obtain analytical expressions for the arrival and service rates of the queues of the two relays and the stability conditions .
Edit intent: clarity
Original:  We quantify the above, analytically for the case of the collision channel and through simulations for the case of Multi-Packet Reception (MPR), and we illustrate when the deployment of a second relay in the system yields significant advantages.
Revised:  We quantify the above, analytically for the case of the collision channel and through simulations for the case of Multi-Packet Reception (MPR), and we provide insight on when the deployment of a second relay in the system yields significant advantages.
Edit intent: clarity
Original:  We quantify the above, analytically for the case of the collision channel and through simulations for the case of Multi-Packet Reception (MPR), and we illustrate when the deployment of a second relay in the system yields significant advantages.
Revised:  We quantify the above, analytically for the case of the collision channel and through simulations for the case of Multi-Packet Reception (MPR), and we illustrate when the deployment of a second relay in the system can yield significant advantages.
Edit intent: clarity
Original: An affiliation network is a particular kind of two-mode social network that consists of a set of `actors' and a set of `events' where ties indicate an actor's participation in an event.
Revised: An affiliation network is a particular type of two-mode social network that consists of a set of `actors' and a set of `events' where ties indicate an actor's participation in an event.
Edit intent: fluency
Original:  While event affiliations are fundamental in defining the social identity of individuals , statistical methods for studying affiliation networks are less well developed than methods for studying one-mode, or actor-actor, networks.
Revised:  Although networks describe a variety of consequential social structures , statistical methods for studying affiliation networks are less well developed than methods for studying one-mode, or actor-actor, networks.
Edit intent: clarity
Original:  In this paper, we extend the bilinear mixed-effects model  developed for one-mode networks to affiliation networks by considering dependence patterns in the interactions between actors and events .
Revised:  In this paper, we extend the bilinear mixed-effects model developed for one-mode networks , to the affiliation network setting by considering the dependence patterns in the interactions between actors and events .
Edit intent: clarity
Original: Conficker is a computer worm which erupted on the Internet in 2008.
Revised: Conficker is a computer worm that erupted on the Internet in 2008.
Edit intent: fluency
Original:  We propose a mathematical model which combines three modes of spreading, local, neighbourhood and global to capture the worm's spreading behaviour.
Revised:  We propose a mathematical model that combines three modes of spreading, local, neighbourhood and global to capture the worm's spreading behaviour.
Edit intent: fluency
Original:  Finally, we show that once the interpretation is fixed, the membership test of a word in the language denoted by a constrained expression is undecidable whereas it is  decidable when the interpretation is not fixed.
Revised:  Finally, we show that once the interpretation is fixed, the membership test of a word in the language denoted by a constrained expression can be undecidable whereas it is decidable when the interpretation is not fixed.
Edit intent: clarity
Original:  Finally, we show that once the interpretation is fixed, the membership test of a word in the language denoted by a constrained expression is undecidable whereas it is  decidable when the interpretation is not fixed.
Revised:  Finally, we show that once the interpretation is fixed, the membership test of a word in the language denoted by a constrained expression is undecidable whereas it is always decidable when the interpretation is not fixed.
Edit intent: clarity
Original:  By expanding the transition probabilities of the Markov process in terms of Poisson-Charlier polynomials, we are able to estimate any moments of the Markov process even though the system of moment equations may not be closed.
Revised:  By expanding the transition probabilities of the Markov process in terms of Poisson-Charlier polynomials, we are able to estimate any moment of the Markov process even though the system of moment equations may not be closed.
Edit intent: fluency
Original:  We ask whether we can add the remaining intervals and construct an extending representation.
Revised:  We ask whether the remaining intervals and construct an extending representation.
Edit intent: clarity
Original:  We ask whether we can add the remaining intervals and construct an extending representation.
Revised:  We ask whether we can add the remaining intervals can be added to create an extending representation.
Edit intent: clarity
Original:  In this paper, we characterize the minimal obstructions which make a partial representation non-extendible.
Revised:  In this paper, we characterize the minimal obstructions which make partial representations non-extendible.
Edit intent: fluency
Original:  This generalizes Lekkerkerker and Boland's characterization of  minimal forbidden induced subgraphs of interval graphs.
Revised:  This generalizes Lekkerkerker and Boland's characterization of the minimal forbidden induced subgraphs of interval graphs.
Edit intent: fluency
Original:  Our characterization leads to a linear-time certifying  for partial representation extension.
Revised:  Our characterization leads to a linear-time certifying algorithm for partial representation extension.
Edit intent: clarity
Original:  We show that the validity problem for propositional dependence logic is NEXPTIME-complete whereas the problem for modal dependence logic and extended modal dependence logic is between NEXPTIME and NEXPTIME^NP.
Revised:  We show that the validity problem for propositional dependence logic is NEXPTIME-complete . In addition, we establish that the corresponding problem for modal dependence logic and extended modal dependence logic is between NEXPTIME and NEXPTIME^NP.
Edit intent: coherence
Original:  The performances of the resulting ABC-random forest methodology are illustrated on several real or realistic population genetics datasets.
Revised:  The performances of the resulting ABC-random forest methodology are illustrated on several population genetics datasets.
Edit intent: clarity
Original:  We continue a recent study into the clique-width of (H_1,H_2)-free graphs and present three new classes of (H_1,H_2)-free graphs that have bounded clique-width .
Revised:  We continue a recent study into the clique-width of (H_1,H_2)-free graphs and present three new classes of (H_1,H_2)-free graphs of bounded clique-width .
Edit intent: clarity
Original:  We also show the implications of our results for the computational complexity of the%DIFDELCMD < {\sc %DIFDELCMD < %%% Colouring problem restricted to (H_1,H_2)-free graphs.
Revised:  We also show the implications of our results for the computational complexity of the%DIFDELCMD < {\sc %DIFDELCMD < %%% problem restricted to (H_1,H_2)-free graphs.
Edit intent: coherence
Original:  To prove boundedness of their clique-width  we develop a technique that is based on bounding clique covering number in combination with reduction to subclasses of perfect  graphs.
Revised:  To prove boundedness of clique-width we develop a technique that is based on bounding clique covering number in combination with reduction to subclasses of perfect graphs.
Edit intent: fluency
Original:  To prove boundedness of their clique-width  we develop a technique that is based on bounding clique covering number in combination with reduction to subclasses of perfect  graphs.
Revised:  To prove boundedness of their clique-width we develop a technique based on bounding clique covering number in combination with reduction to subclasses of perfect graphs.
Edit intent: coherence
Original: In this paper  we consider random access wireless multi-hop mesh networks with multi-packet reception capabilities  where multiple flows are forwarded to the gateways through node disjoint paths.
Revised: In this paper , we consider random access wireless multi-hop mesh networks with multi-packet reception capabilities where multiple flows are forwarded to the gateways through node disjoint paths.
Edit intent: fluency
Original: In this paper  we consider random access wireless multi-hop mesh networks with multi-packet reception capabilities  where multiple flows are forwarded to the gateways through node disjoint paths.
Revised: In this paper we consider random access , wireless, multi-hop mesh networks with multi-packet reception capabilities where multiple flows are forwarded to the gateways through node disjoint paths.
Edit intent: clarity
Original: In this paper  we consider random access wireless multi-hop mesh networks with multi-packet reception capabilities  where multiple flows are forwarded to the gateways through node disjoint paths.
Revised: In this paper we consider random access wireless multi-hop networks, with multi-packet reception capabilities where multiple flows are forwarded to the gateways through node disjoint paths.
Edit intent: clarity
Original: In this paper  we consider random access wireless multi-hop mesh networks with multi-packet reception capabilities  where multiple flows are forwarded to the gateways through node disjoint paths.
Revised: In this paper we consider random access wireless multi-hop mesh networks with multi-packet reception capabilities , where multiple flows are forwarded to the gateways through node disjoint paths.
Edit intent: fluency
Original:  We address the issue of aggregate throughput optimal flow rate allocation with bounded packet delay guarantees for flows exhibiting both intra- and inter-path interference .
Revised:  We explore the issue of aggregate throughput optimal flow rate allocation with bounded packet delay guarantees for flows exhibiting both intra- and inter-path interference .
Edit intent: clarity
Original:  We address the issue of aggregate throughput optimal flow rate allocation with bounded packet delay guarantees for flows exhibiting both intra- and inter-path interference .
Revised:  We address the issue of allocating flow on multiple paths, exhibiting both intra- and inter-path interference .
Edit intent: clarity
Original:  We propose a distributed flow rate allocation scheme that formulates flow rate allocation as an optimization problem and derive the conditions for non-convexity for an illustrative topology .
Revised:  We propose a distributed flow rate allocation scheme that formulates flow rate allocation as an optimization problem . Through an illustrative topology .
Edit intent: coherence
Original:  Furthermore we employ a simplemodel for the average aggregate throughput achieved by all flows  that captures both intra- and inter-path interference  .
Revised:  Furthermore we employ a simplemodel for the average aggregate throughput achieved by all flows , that captures both intra- and inter-path interference .
Edit intent: fluency
Original:  The proposed scheme is evaluated through NS-2 simulations of several random wireless scenarios.
Revised:  The proposed scheme is evaluated through Ns2 simulations of several random wireless scenarios.
Edit intent: fluency
Original:  We also compare in terms of average aggregate throughput our flow allocation scheme with the following schemes: a scheme that assigns flows on paths on a round-robin fashion, one that optimally utilizes the best path only  and another one that assigns the maximum possible flow on each path.
Revised:  We also compare in terms of average aggregate throughput our flow allocation scheme with the following schemes: a scheme that assigns flows on paths on a round-robin fashion, one that optimally utilizes the best path only , and another one that assigns the maximum possible flow on each path.
Edit intent: fluency
Original: The effect of finiteness in degree number is analyzed on a growing network  .
Revised: In this work, a growing network .
Edit intent: clarity