Disease Module Identification DREAM challenge established a framework to evaluate clustering approaches in a biomedical context, by testing the association of communities with GWAS-derived common trait and disease genes. We implemented here several extensions of the MolTi software that detects communities by optimizing multiplex (and monoplex) network modularity. In particular, MolTi now runs a randomized version of the Louvain algorithm, can consider edge and layer weights, and performs recursive clustering.The identification of communities, or modules, is a common operation in the analysis of large biological networks. TheDREAM challenge benchmark, the results strongly depend on the selected GWAS dataset and enrichmentp-value threshold. However, the randomization procedure, as well as the consideration of weighted edges and layers generally increases the number of trait and disease community detected. On simulated networks, the randomization procedure clearly improves the detection of communities. On the The new version of MolTi and the scripts used for the DMI DREAM challenge are available at: https://github.com/gilles-didier/MolTi-DREAM. Thanks to the development of experimental techniques and to the extraction of knowledge accumulated in the literature, biological networks are nowadays assembled on a large scale. A common feature of biological networks is their modularity, i.e., their organization around communities - or functional modules - of tightly connected genes/proteins implicated in the same biological processesThe Disease Module Identification (DMI) DREAM challenge aims at developing a benchmark to investigate different algorithms dedicated to the identification of communities from biological networks3. The challenge has been divided into two sub-challenges, to identify communities either i) from six biological networks independently, or ii) from all these networks jointly. The second sub-challenge, in particular, intend to test if some approaches can leverage complementary information from multiple networks jointly to define integrated communities. The clustering approaches proposed by the participants are assessed regarding their capacity to revealdisease communities, defined as communities significantly associated with genes implicated in diseases in GWAS studies4.5. We focused on the subchallenge dedicated to the identification of communities from multiple networks as MolTi was initially developed to cluster multiplex networks, i.e., networks composed of different layers of interactions. Molti extended the modularity measure to multiplex networks and adapted the Louvain algorithm to optimize this multiplex-modularity. We have demonstrated that this multiplex approach better identifies the communities than approaches merging the networks, or performing consensus clusterings, both on simulated and real biological datasets5.The challengers proposed various strategies and clustering approaches, including kernel clustering, random walks or modularity optimization. We competed with an enhanced version of MolTi, a modularity-based software that we recently developedGrounded on these initial results, we here extended and tested our MolTi software, both on simulated data and on the DMI challenge framework. We improved MolTi with the implementation of a randomization procedure, the consideration of edge and layer weights, and a recursive clustering of the classes larger than a given size.et al., 20155, but also that communities are better detected with the randomization procedure. With the DMI benchmark, we pointed to a great dependence on the GWAS dataset used for the evaluation and on the FDR threshold defined, but, overall, randomizations and edge and layer weights increase the number of disease communities detected.With simulated data, we observed that considering more than one network layer improves the detection of communities, as already noted in Didier5, a modularity-based software. Although MolTi was specifically designed for multiplex networks, , it deals with monoplex networks (i.e. single-layer network) by considering them as multiplex networks composed of a single layer. All the networks are here considered undirected. The new version of MolTi, MolTi-DREAM, and the scripts used for the DMI DREAM challenge are available athttps://github.com/gilles-didier/MolTi-DREAM.We detected communities with an extended version of MolTiModularity. Network modularity was initially designed to measure the quality of a partition into communities6, and subsequently used to find such communities. Since finding the partition optimizing the modularity is NP-complete, we applied the meta-heuristic Louvain algorithm7. This algorithm starts from the community structure that separates all vertices. Next, it tries to move each vertex from its community to another, picks the move that increases modularity the most, and iterates until no change increases the modularity any more. It then replaces the vertices by the detected communities and performs the same operations on the newly obtained graph, until the modularity cannot be increased any more. In order to handle multiplex networks, we use a multiplex-adapted modularity and an adaptation of the Louvain algorithm for optimizing this multiplex-modularity.Edge and layer weights Modularity approaches can deal with weighted networks8, and we modified MolTi to handle weighted networks. We also added the possibility to weight each layer of the multiplex network: the contribution of each layer inMultiplex modularity The modularity measure to detect communities in a multiplex network (Xg)g can be written asXg)( denotes the (monoplex) network of the layerg,wg) multiplex networks contain only dense (resp. sparse) networks, while mixed networks contain both sparse and dense networks. Multiplex networks with missing data are obtained by randomly removing half of the vertices (and the edges involving them) of the multiplex networks simulated from SBMs.We simulated random multiplex networks with a fixed known community structure and various topological properties by using Stochastic Block Models (SBMs) as in Didier10 between the detected communities and the ones used to simulate the multiplex networks.The relevance of a community structure is assessed by computing the adjusted Rand indexBiological Networks. The DMI challenge provided six human biological networks:two protein-protein interactions, one literature-curated signaling, one co-expression, one network linking genes essential for the same cancer types, and one network connecting evolutionary-related genes. These six networks have various sizes and edge densities  and “Final” (104 GWASs), which were used during the challenge, and their union in a “Total” dataset (180 GWASs).Obtaining modules in a given size range. The DMI challenge set up two constraints on the submitted communities: no overlap and a size ranging from 3 to 100 nodes. We here post-filtered all partitions to keeponly classes containing from 7 to 100 nodes.Resolution parameter Modularity-based clustering approaches are often associated to a resolution parameterγ to tune the size of the obtained communities. We tested different values of this parameters , but the leaderboard tests showed clearly better results for the recursive approach. We chose to keep the defaultγ = 1 and focused on this recursive procedure.Recursion procedure We re-clustered all the communities above a certain size (here 100 vertices) by extracting the corresponding subgraphs from the networks and applying recursively the MolTi algorithm. We iterated the process until obtaining only communities with less than 100 vertices, if possible (some communities with more than 100 vertices cannot be split by considering modularity).5 . We observed that considering a greater number of layers always improves the inference of communities, as already observed5 . In addiWe applied the improved MolTi to the networks provided by the DMI challenge (Methods). We focused on the sub-challenge 2, which was dedicated to the identification of communities from multiple networks. We considered the six DMI biological networks as layers of a multiplex network, and applied the recursion procedure to obtain communities in the required size range. The significant disease communities were selected regarding their enrichments in GWAS-associated genes (Methods). We observed first that the number of detected disease communities is strongly dependent on the GWAS dataset and FDR threshold used . For theMultiplex versus monoplex. We next evaluated the added value of the multiplex approach as compared to the identification of modules from the individual networks. When analyzing the significant disease modules obtained for an FDR threshold of 0.1, we observed that combining biological networks in a multiplex generally increases the number of significant modules  is rather likely to blur the signal carried by each network. The DMI biological networks are constructed from different biological sources that might correspond to unrelated community structures. This may explain the results of the sub-challenge 2, in which the top-performer used only the two protein-protein interaction networks. With MolTi, we tried to leverage information from the 6 networks together. However, we do not obtain the highest number of disease modules from a multiplex containing all the six networks, but rather from a subset of these networks.11, which could explain why the co-expression network also provides complementary information. In contrast, the cancer network is determined from processes operating at a very different level. Overall, these results show that the sources of biological information that are added as layers of a multiplex need to be evaluated thoroughly.From a biological perspective, the protein-protein networks and the pathway networks are expected to contain mainly physical or signaling interactions between proteins. It has been shown that interacting proteins tend to be co-expressedp-value-weighted annotations rather than usual binary ones, i.e., “annotated/not annotated”. This probably contributed to the volatility of the results observed with the DMI DREAM challenge framework.Evaluating the relevance of the community structure detected from real-life datasets is a very complicated problem since the actual structure is hidden and generally unknown. In this context, the only possibility for assessing the detected communities is to consider indirect evidence provided by some independent biological information. Different teams are thereby developing proxies to evaluate the communities, mainly based on testing the enrichment of genes contained in each community in Pathways or Gene Ontology annotations. The approach followed by the DMI DREAM challenge is based on GWAS data. This GWAS-based evaluation is specific in the sense that it considershttps://github.com/gilles-didier/MolTi-DREAMMolTi-DREAM and the scripts used for the DMI DREAM challenge:http://doi.org/10.5281/zenodo.146895012Archived scripts and source code for MolTi-DREAM as at time of publication:License for MolTi-DREAM: GNU 3GD designed MolTi and its extensions, AB and AV applied MolTi during and after the challenge. All authors participated in the design of the study, the interpretation of the results and the writing of the manuscript. The authors have diligently addressed my comments and provided detailed discussions on the points I raised. The limitations due to being a companion paper to a flagship study considered in another journal are stated clearly and are reasonable.I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. Gamma=1 could be added next to the Recursion label for clarity in Figures 1-3 in the response"We finished tied for second in the challenge." => We tied for the second place"," is used instead of "." to represent decimal in Tables 2-5 in the responseI thank the authors for their rigorous amendments to the article and the detailed correspondence to the concerns raised by the reviewers. I only have the following minor comments:I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. Identifying communities from multiplex biological networks by randomized optimization of modularity,” Didier et al. apply a network clustering method to identify communities that are significantly enriched in disease signatures. They build on their previously published community detection method, which is based on the greedy optimization  of multiplex modularity. The study is submitted as part of the DMI DREAM Challenge, which aims to evaluate different clustering algorithms by how well the resulting clusters are associated with GWAS-implicated disease genes. The authors test their approach on simulated datasets as well as DMI benchmark datasets. They have three improvements on their original method: randomization, edge and layer weights, and recursive clustering for large clusters.In their manuscript entitled “ The DMI DREAM Challenge itself is an important exercise addressing the non-trivial task of identifying biologically meaningful communities in molecular networks. This paper by Didier et al. takes on this challenge by treating the benchmark datasets as a multiplex network. While limited by the constraints of the challenge, I think the paper is an important contribution that offers an insight as to how multiplex methods fare on real-world biological networks of diverse and not necessarily related sources. The paper is well written, but it has room for improvement, especially in the concise way information is presented in the Methods and Results section. Most of my major comments relate to the clarification of details I thought to be missing from Methods and Results. In various places in the manuscript, the reader is assumed to be familiar with the DREAM Challenge and the previous paper [5] on which this paper is based. The Methods section should thus be expanded to render the study more accessible and self-contained. In some places, the results could be interpreted better. Below are my suggestions meant to help the authors improve the presentation of their study:Major comments: 1) Randomly generated synthetic networks: Even if previously published in [5], it would be helpful if this were described a little more in detail. Providing details about how the community structure is defined or what exactly balanced communities means would be helpful to the reader. 2) More information is needed for the network types, even if they’re described elsewhere under the umbrella of the DMI challenge. What were the sources for each network? Which organism are the PPI networks derived from? Are the co-expression networks tissue-specific or not?  Details like these would be informative when interpreting the results of Figure 3 from a biological standpoint. 3) It is important to clarify how the multiplex network was constructed out of the six networks. For it to be a multiplex network, the same set of nodes should be represented on each layer, which likely requires the pruning of the six benchmark networks. How many nodes did the final multiplex consist of? How many edges were on each layer? Is there any specific inter-layer link structure? 4) The authors use PASCAL to determine the disease-associated genes from GWAS, which are in turn used to determine the communities that are significantly enriched in disease signals. It is crucial at this point to convey to the reader very clearly what PASCAL does and how it’s translated to “significant disease modules.” The authors should, with a couple of sentences, describe how PASCAL does the SNP-to-gene mapping, and then, more importantly, how the p-value weighted gene annotations from PASCAL are used in the enrichment to determine the significant disease modules. A good description of this would facilitate the interpretations of Figure 2-4. 5) The Methods section on controlling the size of modules could be more informative. “We tested different pre-filters (pruning leaves), parameters  and post-filters  in each leaderboard round.” This sentence contains a lot of information without really getting into details. The authors could elaborate on each item. For instance, the resolution parameter does not really seem to come into play (it is even omitted from the definition of multiplex modularity since it is set to 1). Recursion was used to limit the size of the clusters, and while the authors mention tests conducted in leaderboard rounds, no data here is shown as to how varying the resolution parameter changes the results. Perhaps the authors could either omit the section about the resolution parameter altogether or provide some supplementary figures on it. 6) The 100 cutoff is set by the challenge, but in other settings, is there a way to set this ad hoc limit more concretely? Could the authors comment on this? 7) In Figure 1, the authors note that the randomizations improve the accuracy of the detected communities, in particular for dense multiplex networks. This is interesting. May that suggest that dense networks have more possibilities whereby local maxima in the modularity landscape can lead to better results than the best solution? Can the authors comment on possible reasons why this could be the case? 8) What Figure 2 tells me is that if we simply relax the association criterion (FDR cutoff), we’ll simply get more enriched communities, which is not entirely surprising. Here I think the distinction between the different GWAS datasets is important to discuss, if the authors are saying the results are sensitive to the datasets. What is it that makes the “Leaderboard” and “Final” datasets different? What are the diseases and traits included in the GWAS datasets? Perhaps the authors could comment on this. 9) Also for Figure 2 (I may be missing something obvious here) – are these results based on multiplex or monoplex? 10) “We hypothesize that the community structures of these networks (if they exist) are so unrelated that it is pointless to seek for a common structure by integrating them.” This is an interesting point that should remind us that the multiplex biological network should be constructed with a hypothesis in mind (e.g. various molecular levels from transcripts to proteins to metabolites) rather than piling up different networks into a multiplex structure. There is not much reason to think that just adding different sources of biological information should increase the performance of detecting disease modules. The tradeoff between signal and noise with the addition of diverse biological layers can be added as a point of discussion. 11) Multiplex versus monoplex: The notion that multiplex networks help identify a greater number of significant disease modules than monoplex networks combined is an exciting prospect. However, the evidence shown in Figure 3 is a little scant. How was the comparison done exactly? Were the number of significant modules from each separate network summed up and compared to the one from multiplex? These kinds of details should be included. 12) I found the Discussion a bit too DREAM Challenge-oriented. I think the parts comparing the results with those of the top performer are unnecessary . The authors should revise the discussion to recapitulate and interpret their results, and to highlight the advantages of using the multilayer approach. I think it is commendable that the authors chose to include all of the six datasets, regardless of how related they are. Even the fact that the addition of some  layers is detrimental to the outcome is an important finding.   Minor points: 1) In the definition of multiplex modularity: K^(g)_i should be lowercase, i.e. k^(g)_i. 2) Also in the definition of multiplex modularity, I would suggest the authors use s_i instead of k_i if they’re dealing with weights to denote the strength of the node rather than the degree. This is an optional point, but it would make it more aligned with the network science literature and nomenclature.Typos: - “biological networks are nowadays assembled on a large-scale.” --> on a larger scale - “picks the move that increases the most modularity” --> picks the move that increases modularity the most - “data in which we randomly withdrawn vertices” --> data in which we randomly withdraw (or just say remove) vertices - “but to a limited extend after more than four runs” --> to a limited extent - “obtained by considering or not these weights in the MolTi partitioning” --> obtained by considering and not considering these weights in the MolTi partitioningI have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above. In their manuscript entitled “Identifying communities from multiplex biological networks by randomized optimization of modularity,” Didier et al. apply a network clustering method to identify communities that are significantly enriched in disease signatures. They build on their previously published community detection method, which is based on the greedy optimization  of multiplex modularity. The study is submitted as part of the DMI DREAM Challenge, which aims to evaluate different clustering algorithms by how well the resulting clusters are associated with GWAS-implicated disease genes. The authors test their approach on simulated datasets as well as DMI benchmark datasets. They have three improvements on their original method: randomization, edge and layer weights, and recursive clustering for large clusters.The DMI DREAM Challenge itself is an important exercise addressing the non-trivial task of identifying biologically meaningful communities in molecular networks. This paper by Didier et al. takes on this challenge by treating the benchmark datasets as a multiplex network. While limited by the constraints of the challenge, I think the paper is an important contribution that offers an insight as to how multiplex methods fare on real-world biological networks of diverse and not necessarily related sources.The paper is well written, but it has room for improvement, especially in the concise way information is presented in the Methods and Results section. Most of my major comments relate to the clarification of details I thought to be missing from Methods and Results. In various places in the manuscript, the reader is assumed to be familiar with the DREAM Challenge and the previous paper [5] on which this paper is based. The Methods section should thus be expanded to render the study more accessible and self-contained. In some places, the results could be interpreted better. Below are my suggestions meant to help the authors improve the presentation of their study:We agree that our manuscript requires familiarity with the DMI DREAM challenge data and consortium manuscript: It is indeed not independant, and was specifically written as a companion paper to be published with papers from other participants for the F1000 dream challenge channel. We apologize for it’s strong size constraints, and the fact that we tried to avoid any overlap with the main consortium paper, available in bioRxiv and considered for publication in a journal. We checked and tried to give the same amount of details as the other papers published in DREAM channels, in particular in the DMI channel.Major comments:1) Randomly generated synthetic networks: Even if previously published in [5], it would be helpful if this were described a little more in detail. Providing details about how the community structure is defined or what exactly balanced communities means would be helpful to the reader.This point was also stated by another reviewer, and we now have extended the method section describing the generation of random network with a known community structure. We simulated networks with 20 balanced communities, meaning that the communities have the same size (regarding the number of nodes).2) More information is needed for the network types, even if they’re described elsewhere under the umbrella of the DMI challenge. What were the sources for each network? Which organism are the PPI networks derived from? Are the co-expression networks tissue-specific or not? Details like these would be informative when interpreting the results of Figure 3 from a biological standpoint.We agree that more information about the individual networks can help deepening the understanding of some of the results presented in the article, but the networks are an important point and deeply described in the main DMI challenge consortium paper available on biorXiv. This challenge paper is still considered for publication in a journal, and we are expected to avoid any overlap. We however now state in the method section that all the data are human.3) It is important to clarify how the multiplex network was constructed out of the six networks. For it to be a multiplex network, the same set of nodes should be represented on each layer, which likely requires the pruning of the six benchmark networks. How many nodes did the final multiplex consist of? How many edges were on each layer? Is there any specific inter-layer link structure?This is a very important and interesting point. The integration of biological networks obtained from different sources into a multiplex network is indeed not straightforward, as the different networks contain different data. In the multiplex framework, it is not mandatory to prune the networks to get the same set of nodes: multiplex networks share the same set of vertices , as defined in [1]. Each layer provides information for a subset of the nodes, and the information for the remaining nodes is unknown and considered as missing data. In this context, the number of nodes to be clustered is the union of nodes in each layer, not the intersection. It is also in this context that we tested network layers with missing data in the simulations.The multiplex modularity is equal to the sum of the individual modularities of the graphs of the multiplex with regard to the same community partition. Therefore, there is no need for an inter-layer link structure when constructing the multiplex network.                                                                                [1] Kivelä M, Arenas A, Barthelemy M, Gleeson JP, Moreno Y, Porter MA. 2014. Multilayer networks. Journal of Complex Networks 2:203–2714) The authors use PASCAL to determine the disease-associated genes from GWAS, which are in turn used to determine the communities that are significantly enriched in disease signals. It is crucial at this point to convey to the reader very clearly what PASCAL does and how it’s translated to “significant disease modules.” The authors should, with a couple of sentences, describe how PASCAL does the SNP-to-gene mapping, and then, more importantly, how the p-value weighted gene annotations from PASCAL are used in the enrichment to determine the significant disease modules. A good description of this would facilitate the interpretations of Figure 2-4.We rephrased the corresponding method section to mention p-value and multiple testing corrections. However, we have for this companion paper a strong size constraints. The PASCAL tool is a complex approach deeply described in a publication , and its application and use in the context of the DMI dream challenge is fully described in the consortium paper. A precise and correct description of the evaluation procedure, from SNP mapping to significant modules would be too long and overlapping with the consortium and PASCAL papers.5) The Methods section on controlling the size of modules could be more informative. “We tested different pre-filters (pruning leaves), parameters  and post-filters  in each leaderboard round.” This sentence contains a lot of information without really getting into details. The authors could elaborate on each item. For instance, the resolution parameter does not really seem to come into play (it is even omitted from the definition of multiplex modularity since it is set to 1). Recursion was used to limit the size of the clusters, and while the authors mention tests conducted in leaderboard rounds, no data here is shown as to how varying the resolution parameter changes the results. Perhaps the authors could either omit the section about the resolution parameter altogether or provide some supplementary figures on it.Indeed, the resolution parameter was missing in the equation, and we now have included it. In addition, we removed from the manuscript the sentence describing the various test we made as this was indeed possibly confusing.Concerning the choice of the default resolution parameter, we made extensive tests that are provided below, but we lack space in the manuscript to detail them. These tests show that the recursion approach provides overall a higher number of significant disease modules in the Dream Module Identification (DMI) challenge framework.Total number of modules obtained when running Molti with 10 randomizations on the 6 DMI challenge network for different values of the resolution parameter:Table 1Number of significant Modules obtained with variations of Gamma:Table 2Comparison with recursion (apply Molti in a recursive way to communities larger than 100):Table 3                                                    For FDR= 0.1Figure 1For FDR = 0.05Figure 2For FDR = 0.01Figure 36) The 100 cutoff is set by the challenge, but in other settings, is there a way to set this ad hoc limit more concretely? Could the authors comment on this?Defining the optimal module size is a complex task. One could imagine using the challenge benchmark to find the optimal module size. However, this is not feasible in practice as 1) the computation of PASCAL scores are time-consuming and cannot really be used to optimize the algorithms, 2) the sensitivity/volatility of the results to the number of submitted modules and GWAS data used make the interpretation on a fine-grained scale difficult.The consortium paper discuss this point and identify, in particular, that the average module size do not correlate with the number of significant modules identified by the different approaches . It is also interesting to note that some modules are submodules of larger modules.7) In Figure 1, the authors note that the randomizations improve the accuracy of the detected communities, in particular for dense multiplex networks. This is interesting. May that suggest that dense networks have more possibilities whereby local maxima in the modularity landscape can lead to better results than the best solution? Can the authors comment on possible reasons why this could be the case?This is a very interesting point. We were actually surprised by the extent to which randomization improves the community detection on simulated networks. We initially thought that the greater increase in the accuracy of the communities detected on dense multiplex networks came from the fact that there was more room for improvement in this case. Your point makes sense since one can expect a greater number of local maxima for the modularity for dense network than for sparse ones, in addition to more possibilities of moving vertices during the Louvain execution. This point definitely deserves to be further investigated.8) What Figure 2 tells me is that if we simply relax the association criterion (FDR cutoff), we’ll simply get more enriched communities, which is not entirely surprising. Here I think the distinction between the different GWAS datasets is important to discuss, if the authors are saying the results are sensitive to the datasets. What is it that makes the “Leaderboard” and “Final” datasets different? What are the diseases and traits included in the GWAS datasets? Perhaps the authors could comment on this.The number of significant communities increases when the FDR cutoff is larger, as expected. However, the results are also quite sensitive to the dataset considered as pointed out by the reviewer. The different GWAS datasets were chosen by the DREAM challenge organizers, and splited into “Leaderboard” and “Final” manually. A detailed discussion of the diseases and traits included in the GWAS datasets, as well as their comparison, is proposed in the DMI consortium manuscript  and cannot be reproduced here.9) Also for Figure 2 (I may be missing something obvious here) – are these results based on multiplex or monoplex?In order to clarify this point, we now state in the figure caption that the results are based on the multiplex networks.10) “We hypothesize that the community structures of these networks (if they exist) are so unrelated that it is pointless to seek for a common structure by integrating them.” This is an interesting point that should remind us that the multiplex biological network should be constructed with a hypothesis in mind (e.g. various molecular levels from transcripts to proteins to metabolites) rather than piling up different networks into a multiplex structure. There is not much reason to think that just adding different sources of biological information should increase the performance of detecting disease modules. The tradeoff between signal and noise with the addition of diverse biological layers can be added as a point of discussion.Thanks for this interesting remark. We agree that multiplex biological networks should be constructed with a hypothesis in mind, and that the network that are piled up in a multiplex are expected to be realisations of the true underlying biological modules. This is the case for the two PPI network and the pathway network that are expected to represent cellular processes. In addition, pairs of proteins belonging to the same pathway or co-expressed are more likely to physically interact than pairs of random proteins [1]. Therefore, even if the biological information contained in co-expression or pathways networks is completely different to the one contained in PPI networks, they still can improve the detection of the communities by adding more signal to the system and reducing the bias and noise of individual networks as we previously demonstrated [2]. The cancer network, contrarily, might contain very different biological information.However, concerning the bias and noise present in the different networks, as the bias and noise are not the same, we see the combination of the different sources in a more positive way, as not adding noise but complementing each other to reduce noise. For instance, if we take individual PPI networks obtained from different sources and we integrate them into a multiplex PPI network, we expect to obtain better clustering results than with the individual networks alone. All these monoplex PPI networks try to reflect the real PPI network containing all the human genes, all their interactions and their real community structure. However, they have missing data and they strongly depend on the technologies used to get the interactions (bias and noise). Therefore, since all of them attend to reflect the same system, the biological signal increases and the noise and missing data tend to reduce. We added a sentence to the discussion concerning this point.[1] Rual JF, Venkatesan K, Hao T, et al.: Towards a proteome-scale map of the human protein-protein interaction network. Nature. 2005; 437(7062): 1173–1178.[2] Didier G, Brun C, Baudot A: Identifying Communities from Multiplex Biological Networks. PeerJ. 2015; 3: e1525.11) Multiplex versus monoplex: The notion that multiplex networks help identify a greater number of significant disease modules than monoplex networks combined is an exciting prospect. However, the evidence shown in Figure 3 is a little scant. How was the comparison done exactly? Were the number of significant modules from each separate network summed up and compared to the one from multiplex? These kinds of details should be included.The comparison between the different approaches is done following the DMI challenge benchmark, that is by computing the number of significant disease modules (with a FDR threshold of 0.1). We computed this number of significant modules identified from the 6 biological networks independently, and then from combination of networks thanks to the multiplex framework . We used combinations of 2 to 6 networks, considered as multiplex networks of 2 to 6 layers.12) I found the Discussion a bit too DREAM Challenge-oriented. I think the parts comparing the results with those of the top performer are unnecessary . The authors should revise the discussion to recapitulate and interpret their results, and to highlight the advantages of using the multilayer approach. I think it is commendable that the authors chose to include all of the six datasets, regardless of how related they are. Even the fact that the addition of some  layers is detrimental to the outcome is an important finding.The manuscript is indeed DREAM challenge oriented as it is not an independent manuscript but a companion paper. Regarding the interpretation of the multiplex approach, we think it is important to state that the top-performers selected a subset of the 6 networks, reflecting also the reviewer’s comment on the choice of the network to be piled up. We agree that a lot could still be discussed regarding our (and others) obtained results in this challenge, and extended a bit the discussion. This point is also discussed in the challenge consortium manuscript.Minor points:1) In the definition of multiplex modularity: K^(g)_i should be lowercase, i.e. k^(g)_i.Thanks for pointing this out, it has been changed to s following your next comment.2) Also in the definition of multiplex modularity, I would suggest the authors use s_i instead of k_i if they’re dealing with weights to denote the strength of the node rather than the degree. This is an optional point, but it would make it more aligned with the network science literature and nomenclature.DoneTypos:Thanks for pointing all these typos !- “biological networks are nowadays assembled on a large-scale.” --> on a larger scaleDone- “picks the move that increases the most modularity” --> picks the move that increases modularity the mostDone- “data in which we randomly withdrawn vertices” --> data in which we randomly withdraw (or just say remove) verticesDone- “but to a limited extend after more than four runs” --> to a limited extentThis sentence has been removed after other reviewer’s comment.- “obtained by considering or not these weights in the MolTi partitioning” --> obtained by considering and not considering these weights in the MolTi partitioningDone Overview The paper presents: 1. a couple of improvements over the method in the authors' previous 2015 paper on multiplexed modularity, and 2. the application of this improved method to the Disease Module Identification DREAM challenge.Method The paper adequately describes the incremental improvement of the general method over the previous paper regarding the following. 1. The algorithm randomly selects one of the moves improving the modularity at every stage. I assume this helps the method to arrive at different local minima for each run, thereby improving its performance on the nonlinear modularity surface. 2. The incorporation of edge and graph weights into the definition of modularity. Both of these points are well justified, and presented in adequate detail. The only minor detail that is missing is that Equation 1 does not include the resolution parameter.Results and Performance Evaluation The improvement in performance due to randomization is presented in Figure 1, while Figure 4 presents evidence of improvement due to the graph (layer) weights. The improvement due to edge weights is not presented, but it logically follows that any network model wherein edges with larger weights are likely to form within modules will show improved performance under a weighted definition of modularity. The authors did not have control over the DREAM challenge evaluation, but a reader might have a few questions regarding the performance evaluation. For example, if the judging criterion is the number of significantly GWAS associated modules, does the score improve by dividing one large disease associated module into two, if they both are still significant? Presentaion Other than the missing resolution parameter, the method is adequately presented. There were a few minor issues with language. For example:ies detected." 1. The second paragraph of the abstract should end with "the number of trait and disease communitwithdrawn vertices of each layer ..." 2. While describing the method of simulating the missing data, another form of the word should be used instead of " ... we randomly The authors provide source code for both the latest version, and also the version that was used for the DREAM challenge. It would be helpful if the authors also provide, if those are readily available, the scripts that were used to run the DREAM and simulated data for the results presented. This will help answer minor questions regarding details like filtering etc.Conclusion and suggestions I think the method described by the paper is scientifically valid and its presentation is adequate, other than the minor issues raised above. Some of the important questions that may be pursued further are related to the selection of the graph weights. Currently, the weights are selected arbitrarily using the relative performance of the individual networks on predicting the disease modules. Could there be a more systematic manner of weight selection based on both the congruency with what's known of the true modules and the relative redundancy in the various layers?I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. The paper presents:1. a couple of improvements over the method in the authors' previous 2015 paper on multiplexed modularity, and2. the application of this improved method to the Disease Module Identification DREAM challenge. Method The paper adequately describes the incremental improvement of the general method over the previous paper regarding the following.1. The algorithm randomly selects one of the moves improving the modularity at every stage. I assume this helps the method to arrive at different local minima for each run, thereby improving its performance on the nonlinear modularity surface.2. The incorporation of edge and graph weights into the definition of modularity. Both of these points are well justified, and presented in adequate detail. The only minor detail that is missing is that Equation 1 does not include the resolution parameter.Thanks for pointing out this omission. The resolution parameter has been included to the Equation 1 in the revised version of the manuscript.Results and Performance Evaluation The improvement in performance due to randomization is presented in Figure 1, while Figure 4 presents evidence of improvement due to the graph (layer) weights. The improvement due to edge weights is not presented, but it logically follows that any network model wherein edges with larger weights are likely to form within modules will show improved performance under a weighted definition of modularity.The tests of edge weights is indeed not presented as a figure, but some data are summarized as a table (Table 2).The authors did not have control over the DREAM challenge evaluation, but a reader might have a few questions regarding the performance evaluation. For example, if the judging criterion is the number of significantly GWAS associated modules, does the score improve by dividing one large disease associated module into two, if they both are still significant? per se.This is a tricky question. Briefly, the DREAM evaluation uses the PASCAL tool to compute a score for each modules according to their enrichments in GWAS-significant genes. The number of significant disease module in a given partition is then computed according to an enrichment threshold, and considering correction for multiple testing. In this context, the total number of submitted valid communities is important, as submitting more modules will induce a stronger correction for multiple testing. It is thereby not straightforward to evaluate if dividing a large disease module into two will lead to two submodules both still significant, as this will also increase the correction for multiple testing. In other words, submitting more modules can affect badly the results even if without multiple testing correction it would have increased the number of significant disease modules. The PASCAL tool also takes into account the GWAS statistics to compute the significance, it is thus overall very hard to use the obtained discrete results  to tune/optimize slight variations of the approach, as the variability in the results can come from many factors. Some of these points are discussed in the DMI challenge manuscript as some of the top-performers of the subchallenge 1 selected the modules based on their sizes without working on the improvement of the algorithmsPresentaion Other than the missing resolution parameter, the method is adequately presented. There were a few minor issues with language. For example:ies detected."1. The second paragraph of the abstract should end with "the number of trait and disease communitCorrectedwithdrawn vertices of each layer ..."2. While describing the method of simulating the missing data, another form of the word should be used instead of " ... we randomlyWe changed the instances of “withdraw” to “remove”The authors provide source code for both the latest version, and also the version that was used for the DREAM challenge. It would be helpful if the authors also provide, if those are readily available, the scripts that were used to run the DREAM and simulated data for the results presented. This will help answer minor questions regarding details like filtering etc.The scripts used to run the DREAM challenge approaches are all available from the challenge webpages as a community resource.Conclusion and suggestions I think the method described by the paper is scientifically valid and its presentation is adequate, other than the minor issues raised above. Some of the important questions that may be pursued further are related to the selection of the graph weights. Currently, the weights are selected arbitrarily using the relative performance of the individual networks on predicting the disease modules. Could there be a more systematic manner of weight selection based on both the congruency with what's known of the true modules and the relative redundancy in the various layers?This is a very interesting question. As noted by the reviewer, we selected the weights based on the relative performance on the individual networks. However, this could not be done in a more systematic way, as true modules are not known . Another approach could be to weight the different layers based on our a priori knowledge/trust of the different layers. However, we have difficulties understanding how it would be possible in practice to weight according to the relative redundancy of the various layers. The authors explain the method that underlies their submission to the 2016 DREAM Disease Module Identification challenge. The authors only discuss their results from subchallenge 2; they should either say this is what they are going to do up front or also mention their performance on subchallenge 1. The paper is not self-contained, it already assumes some familiarity with the setup of the challenge; since this is being published in a collection on F1000 related to the dream challenge, perhaps that is appropriate, however I would have preferred if the authors had spent more time describing the challenge:  i.e. what does it mean in more detail to identify communities from the six biological networks jointly, rather than independently?γ but this parameter is defined nowhere in their paper: is this a parameter of the GenLouvain method to which they refer? While the authors release their code, which is commendable, there are not sufficient details in the text to completely understand their methods without returning to the code. For example, they talk about a resolution parameter The authors present a randomized algorithm which they run from 1 to 10 times, and return the partition with highest modularity, but figure 1 uses only 1 to 5 randomization runs. Furthermore, the authors do not explain how the parameter "5" or "10" is selected. There are other method details that involve parameters that are missing, for example in their set of simulated networks, it is impossible to discover how they set their parameters from just this writeup: They write "we simulated random multiplex networks with a fixed known community structure,... and various topological properties " Is this the same collection of simulated networks that they generated in a previous paper (reference 5 that they cite?) if so, please say this explicitly. Even the writeup in reference 5 is somewhat sketchy, but it's better than what is here. The authors conclude that the power of including multiplex networks is dependent perhaps on the networks being generated from partial views of the same underlying community structure; when networks 5 and 6, which were very different were included, the performance of their method degraded, and this was found across the challenge in general.I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above. The authors explain the method that underlies their submission to the 2016 DREAM Disease Module Identification challenge. The authors only discuss their results from subchallenge 2; they should either say this is what they are going to do up front or also mention their performance on subchallenge 1. We indeed focused on subchallenge 2. During the challenge leaderboard phase, our consortium tested many very different approaches on subchallenge 1, and we did not evaluate Molti thoroughly in this subchallenge. In addition, Molti was specifically designed to leverage multiplex networks. We added a sentence (highlighted in blue) to the manuscript to state this point more clearly.The paper is not self-contained, it already assumes some familiarity with the setup of the challenge; since this is being published in a collection on F1000 related to the dream challenge, perhaps that is appropriate, however I would have preferred if the authors had spent more time describing the challenge: i.e. what does it mean in more detail to identify communities from the six biological networks jointly, rather than independently? We agree that our manuscript was specifically written for the F1000 dream challenge channel: it has strong size constraints and requires some familiarity with the challenge. The consortium manuscript is available in bioRxiv, and is still under consideration for publication in a journal. We wanted to avoid any potential overlap in the interpretation of the results in between the consortium paper and our manuscript. We finally also checked other papers published in DREAM channels and tried to give the same level of details. We however extended the description of the DREAM sub-challenge 2 in the main text.γ but this parameter is defined nowhere in their paper: is this a parameter of the GenLouvain method to which they refer?While the authors release their code, which is commendable, there are not sufficient details in the text to completely understand their methods without returning to the code. For example, they talk about a resolution parameter Thanks for pointing this out. Indeed, we had forgotten the γ parameter and its description in the method section. The γ parameter is a resolution parameter allowing to tune the size of the obtained communities. Increasing this parameter allows reducing the size of the obtained communities. We now present the results obtained by tuning this parameter instead of applying the recursion in the answer to another referee. We also extended the description of the code in the github repo and the description of the simulated networks with SBM to answer the comment below.The authors present a randomized algorithm which they run from 1 to 10 times, and return the partition with highest modularity, but figure 1 uses only 1 to 5 randomization runs. Furthermore, the authors do not explain how the parameter "5" or "10" is selected. There are other method details that involve parameters that are missing, for example in their set of simulated networks, it is impossible to discover how they set their parameters from just this writeup: They write "we simulated random multiplex networks with a fixed known community structure,... and various topological properties " Is this the same collection of simulated networks that they generated in a previous paper (reference 5 that they cite?) if so, please say this explicitly. Even the writeup in reference 5 is somewhat sketchy, but it's better than what is here.Number of randomizations We agree that the different number of randomizations used along the manuscript can be confusing. We tried to make this point clearer in the revised version. The number of randomizations needed for a given dataset is not easy to seta priori. Since increasing the number of randomizations improves the modularity - and hopefully the accuracy - of the communities detected, we basically increased the number of randomization until obtaining no significant change in the communities detected. For the simulations, we selected 5 randomizations because the adjusted Rand index plot for 5 randomizations is confounded with that for 4 randomizations. For the Dream Challenge dataset, we considered 10 randomizations because increasing this number was too heavy in computation time.Simulated networks with a community structure The method section has been extended to describe SBM network simulations more precisely. These random networks are generated with the same protocol as the one described in reference 5, but were re-generated for this project. In addition, the code to generate the multiplex networks with SBM (and detect and compare the communities with adjusted Rand index) is now available on the github repository. Didier and colleagues present MolTi-DREAM, an update to their previous software for community detection in multiplex networks and its application to the disease module discovery using synthetic and DREAM challenge data. The new version of the software adds the possibility of edge and layer weights, the randomization of the underlying Louvain algorithm and partitioning of large modules into smaller modules based on user defined parameters. Based on their analysis of simulated and biological interaction data, they reaffirm that using multiple layers of networks and randomized repetition of module discovery could improve the accuracy. Overall the article is clearly written and the technical details are clearly explained with several exceptions I mention below: 1. The multiplex modularity formula lacks the resolution parameter (which should appear before ki kj / 2m in the summation). The authors are encouraged to provide data / figures with respect to the reasoning on the selection of the default resolution parameter . 2. Randomization procedure is unclear. I believe the cost function used is the multiplex modularity given in Eq 1 (L) but the “move” leading to an increase of the modularity is not formally stated ). The choice of 4 by default is also somewhat arbitrary given that the difference between 3,4,5 are all very small. The significance of the difference in Rand index across runs in Figure 1 could be used to decide the number after which the change is not significant. 3. The simulation of the multiplex networks could be explained better. Potentially owing to the previous publication, there is no detail in regards to which model was used to generate these networks. A brief description of SBMs and the underlying assumptions of the model it relies on would help. Are these simulated networks are more ER-like? Could this be the reason why the simulated results do not reflect the results on the real networks? Also, it would certainly be useful to add the standard deviation across 2000 networks in Figure 1. I had difficulties following how exactly the mixed and noisy networks are generated . 4. The coverage / precision of disease module discovery is missing. What is the number of all modules identified by the algorithm, how many disease modules are there (or could there be) in total? The latter question could be tricky to answer but I believe a lower and upper bound could be provided . 5. “combining biological networks in a multiplex generally increases the number of significant modules”. The Figure 3 does not exactly reflect this, it seems the number of significant modules for multiplex < monoplex(ppi1) + monoplex(ppi2). Maybe the authors could show the numbers for the union of the modules identified using ppi1and ppi2 and put that into the figure as to what to expect when the modules are combined using these networks separately. 6. The choice of the for each biological network seems rather arbitrary. Could these weights be optimized (i.e. using leaderboard data) and their effect be tested on final data? 7. “the community structure of these networks (if they exist) are so unrelated that it is pointless to seek for a common structure by integrating them” I feel that this statement should be supported by further evidence. Could the authors provide some measures in regards to the modularity of each of these networks and the overlap of nodes / edges between them. This would also help to justify the argument on the “DMI biological networks are constructed from different biological sources that might correspond to unrelated community structures”. Minor: Explain what monoplex network means at its first occurrence for readers not familiar with terminology. “hande mulxtiplexes” multiplex networks “following the PASCAL tool” identified using “Considering a greater number of layers...” lacks the main clause / verb “after more than four runs” upto four runs / repetitions “varies in a non-trivial way” non-trivial?I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above. 1. The multiplex modularity formula lacks the resolution parameter (which should appear before ki kj / 2m in the summation). The authors are encouraged to provide data / figures with respect to the reasoning on the selection of the default resolution parameter .Indeed, the resolution parameter was lacking in the formula. We now have corrected this. Concerning the choice of the default resolution parameter, we made extensive tests that are provided below, but we lack space in the manuscript to detail them. These tests show that the recursion approach provides overall a higher number of significant disease modules in the Dream Module Identification (DMI) challenge framework.Total number of modules obtained when running Molti with 10 randomizations on the 6 DMI challenge network for different values of the resolution parameter:Table 1Number of significant Modules obtained with variations of Gamma:Table 2Table 3Table 4Comparison with recursion (apply Molti in a recursive way to communities larger than 100):Table 5  For FDR= 0.1Figure 1For FDR = 0.05Figure 2For FDR = 0.01Figure 32. Randomization procedure is unclear. I believe the cost function used is the multiplex modularity given in Eq 1 (L) but the “move” leading to an increase of the modularity is not formally stated ). The choice of 4 by default is also somewhat arbitrary given that the difference between 3,4,5 are all very small. The significance of the difference in Rand index across runs in Figure 1 could be used to decide the number after which the change is not significant.The cost function is indeed the multiplex-modularity given in Eq 1. At each step, all the moves of an element from a community to another that lead to an increase of the multiplex-modularity are considered, and one of them is randomly picked with a uniform probability. The final number of randomizations was arbitrarily chosen, but several were tested during the Challenge.The choice of 4 randomizations by default was indeed arbitrary, and we removed this sentence in the manuscript to just state that this number is user-defined. The significance of the difference in Rand indexes can also be used to select a correct number of randomizations. However, since the adjusted Rand index is computed with regard to the real communities, it could be used only when the real communities are known, i.e. in our random network simulations. For the real biological networks provided by the challenge, the actual community structure is unknown.Increasing the number of randomizations cannot harm (except with regard to the computation time) since the modularity of the detected communities increases with this number. A possibility could be to test the significance of the modularity increase between two successive numbers of randomizations. However, computing this significance is complex and time-consuming for large networks.3. The simulation of the multiplex networks could be explained better. Potentially owing to the previous publication, there is no detail in regards to which model was used to generate these networks. A brief description of SBMs and the underlying assumptions of the model it relies on would help. Are these simulated networks are more ER-like? Could this be the reason why the simulated results do not reflect the results on the real networks? Also, it would certainly be useful to add the standard deviation across 2000 networks in Figure 1. I had difficulties following how exactly the mixed and noisy networks are generated .Indeed, the simulations have been described in our previous publication, but the current version was lacking details. We extended the method section to describe more precisely how the simulated networks with a known community structure, and their variations are generated.As detailed in the revision, a key property of the SBMs is that, given a community structure, each edge is drawn independently with a probability that depends only the community to which its nodes belong. These property is certainly not granted in biological networks but random graph models taking into account dependance between edges  are difficult to estimate and to simulate. We considered simple SBMs parameterized with a probability for edges between nodes in a same community (intra-community edges) and a probability for edge between nodes belonging to two different communities (inter-community edges). Networks obtained from SBMs are generally not homogeneous, thus quite different from ER ones. The software performing the simulation of multiplex networks from SBMs, called “simul” is now available in the GitHub repository.We tried to display the standard deviation of the adjusted Rand index, but the result was quite confusing since the the error bars tend to overlap themselves (see below for the simulated sparse and dense networks).Figure 4Figure 54. The coverage / precision of disease module discovery is missing. What is the number of all modules identified by the algorithm, how many disease modules are there (or could there be) in total? The latter question could be tricky to answer but I believe a lower and upper bound could be provided .Indeed, the total number of discovered modules was not detailed in the manuscript. It was however used by the PASCAL tool to compute the number of significant disease modules, as the total number of submitted modules is used to correct for multiple testing. We added the total number of discovered valid modules (of size [7-100]) to the figure and table captions.Figure 2. The numbers used in the Figure 2  have been added to the caption.Table 6Figure 3: Table 7Number of total modules detected by Molti for the results presented on:Table 2: (nRandom = 10). These numbers have been added to the Table 2 caption No Weights <- 615 Figure 4: (nRandom = 10).These numbers have been added to the Figure caption. No Weights <- 585Weights <- 585Confidence Weights <- 555Inverse Confidence Weights <- 648The question of how many disease modules exist or could exist is indeed tricky to answer, and is partly discussed in the DMI challenge consortium paper. In this challenge manuscript, the full detail on the 180 GWAS disease/trait datasets, their classification, as well as the scoring method are detailed. Briefly, a module is considered significant if it is enriched in at least one GWAS-associated trait or disease according to the PASCAL approach. A sampling approach is also used to account for robustness in comparing the challengers’ results. The figures 1, 3 and 4 of the consortium paper are in particular and attempt to dig in the reviewer’s proposed direction.https://www.biorxiv.org/content/early/2018/02/15/2655535. “combining biological networks in a multiplex generally increases the number of significant modules”. The Figure 3 does not exactly reflect this, it seems the number of significant modules for multiplex < monoplex(ppi1) + monoplex(ppi2). Maybe the authors could show the numbers for the union of the modules identified using ppi1and ppi2 and put that into the figure as to what to expect when the modules are combined using these networks separately.The modules identified by the multiplex approach cannot be directly compared to the sum of the modules identified independently in the monoplex networks, as the communities might be the sames or very similar. In principle, the two PPI networks should detect similar communities, since they are supposed to contain biological information of the same nature. However, both networks are built from different sources, each one with different features or missing data. Therefore, their combination into a multiplex network should lead to a closer representation of the “real PPI network”, and is expected to result in the detection of a larger number of more accurate communities. In order to compare the communities detected by the two monoplex PPI networks individually with the communities identified when these networks are integrated into a 2-layer multiplex network, we computed the adjusted Rand index  [1] between the three corresponding partitions. The adjusted Rand index is the corrected-for-chance version of the Rand index, which is a measure of the similarity between two data clustering [2].  It is usually applied to compare partitions obtained by different clustering algorithms on the same network. Nevertheless, it can be applied to our problem by considering the common nodes between every pair of monoplex network .The results are displayed below in a table and a figure:PPI_1 PPI_2 PPI1_+_PPI2PPI_11.0000000 0.1075211 0.2645176PPI_2 0.10752111.0000000 0.2906837PPI1_+_PPI2 0.2645176 0.29068371.0000000Figure 6PPI1_+_PPI2) and 2*RandIndex < RandIndex. Therefore, it seems that the multiplex approach can reflect better the “real” community structure of the “real PPI” than the addition of both single networks. Finally, the community partition of the multiplex is closer to the one of the PPI_2 than to the one of the PPI_1.These results show that the community structure obtained from the multiplex approach is closer to the ones found with both single PPIs. In other words, the communities obtained from single PPI networks are closer to the multiplex than to the communities obtained from the other single network. In addition, 2*RandIndex < RandIndex and their effect be tested on final data?We indeed considered different optimizations of the weights. This point was not clearly stated in the manuscript, but the weights were chosen based on the number of significant modules obtained in the application of Molti on the isolated monoplex networks. We rephrased the corresponding sentence to clarify this.a posteriori that the results of the leaderboard can be used to choose the best weights in the final data : the results obtained using the Leaderboard and the Final GWAS datasets  are not clearly correlated, making difficult to optimize the weights from the Leaderboard results. In addition, the evaluation of the significance of the results by a discrete number of significant disease modules is strongly sensitive to the number of submitted modules, because of the correction for multiple testing. This volatility makes the benchmark difficult to use to evaluate subtle changes in the methods. That’s why we implemented and tested our approach on the simulated networks. Unfortunately, the simulated networks cannot be used to evaluate weights.However, we do not think7. “the community structure of these networks (if they exist) are so unrelated that it is pointless to seek for a common structure by integrating them” I feel that this statement should be supported by further evidence. Could the authors provide some measures in regards to the modularity of each of these networks and the overlap of nodes / edges between them. This would also help to justify the argument on the “DMI biological networks are constructed from different biological sources that might correspond to unrelated community structures”.The modularity is a measure that needs to be computed on a community structure, hence we need first to partition the networks to compute the modularity. To evaluate the modularity of the considered biological networks, we applied Molti with default parameters on the individual networks  to obtain the network partitions. We then computed the adjusted Rand index [1] in between the 6 network partitions. Here also, the adjusted Rand index is applied to our problem by considering the common nodes between every pair of monoplex network .The Adjusted Rand Index computed for every pair of partitions of the monoplex networks provided by Molti (10 randomizations) are displayed in the following table and figure:    PPI_1  PPI_2  PATH_3  COEX_4 CANCER_5  HOMO_6PPI_11.000000000 0.107521064 0.082823431 0.012937084 0.004922555 0.051958946PPI_2 0.1075210641.000000000 0.091792998 0.010104981 0.004755694 0.023984747PATH_3 0.082823431 0.0917929981.000000000 0.007815447 0.001958814 0.024252282COEX_4 0.012937084 0.010104981 0.0078154471.000000000 0.002040522 0.006049318CANCER_5 0.004922555 0.004755694 0.001958814 0.0020405221.000000000 0.002211310HOMO_6 0.051958946 0.023984747 0.024252282 0.006049318 0.0022113101.000000000Figure 7The two PPI networks are the most similar in terms of communities structure, as expected. The community structure of the Pathways network is also quite similar to both PPIs, which makes sense since proteins in the same pathway are more likely to interact physically than those belonging to different pathways. In addition, the Homology network is more similar to those three networks than the Co-expression network. This might come from the fact that this homology network is built by expanding known pathways (Kegg in particular) with the addition of new member related by eukaryotic homology, as detailed in the challenge consortium manuscript. The partition the most different is the one obtained from the cancer network.[1] Santos J, Embrechts M. 2009. On the use of the adjusted rand index as a metric for evaluating supervised classification. In: Alippi C, Polycarpou M, Panayiotou C, Ellinas G, eds. Artificial neural networks—ICANN 2009. Lecture notes in computer science, vol. 5769. Berlin Heidelberg: Springer, 175–184.Journal of the American StatisticalAssociation. American Statistical Association. 66 (336): 846–850.doi:10.2307/2284239.JSTOR 2284239. [2] W. M. Rand (1971). "Objective criteria for the evaluation of clustering methods".Minor:Explain what monoplex network means at its first occurrence for readers not familiar with terminology.OK, done in the method section“hande mulxtiplexes” multiplex networksOK, all occurrences of “multiplexes” have been changed to “multiplex networks”“following the PASCAL tool” identified usingChanged “following” to “using”“Considering a greater number of layers...” lacks the main clause / verbOK, changed to “We observed that considering a greater …”“after more than four runs” upto four runs / repetitionsOK, changed to “Increasing the number of randomization runs improves the results up to four runs.”“varies in a non-trivial way” non-trivial?OK, we changed to “is strongly dependent“. This expression was related to the fact that we do not observe a clear correlation between the results obtained on the leaderboard and final GWAS datasets.


Embryo transfer (ET) is a key step of assisted reproductive procedures, where the transferred medium containing the embryos is injected into the uterine cavity through a transcervical catheter and blended with intrauterine fluid in the uterine cavity. This procedure determines the delivery sites of embryos in the uterine cavity and has crucial impact on the implantation. Due to practical restrictions and ethical issues, it is often difficult to perform an in vivo study in humans to examine factors that affect the motions and delivery of embryos during ET. Alternatively, mathematical modeling is a powerful tool to that end.A computational model is developed to simulate the intrauterine mixing flow and track the embryo motions. Two important factors affecting the intrauterine flow are studied via this model: the viscosity of the transferred medium and the injection speed. Numerical results show that the dispersion pattern and the final delivery sites of the embryos are significantly influenced by the viscosity of the transferred medium. Specially, increasing the transferred medium viscosity close to that of the uterine fluid can enhance the probability that the embryos are delivered close to the fundus and keep them from being dragged backward to the cervix during catheter withdrawal. In addition, a slow injection speed can lower the driving force on the embryo during ET, which can prevent the embryo from being injured.Based on our study, the practice of using a transferred medium with similar viscosity to that of the uterine fluid and a slow injection speed is recommended for real embryo transfer procedures in clinic. Embryo transfer (ET) is the last step of assisted reproduction procedures. During ET, a catheter is loaded with the transfer medium containing 1–5 embryos, inserted into the uterine cavity via the cervical canal, and then injected its loading and withdrawn from the uterine cavity immediately. Despite the successful in vitro fertilization (IVF) rate of greater than 80% in laboratory, the pregnancy rate per ET is unfortunately as low as 44% [Several factors have a significant influence on the pregnancy rate of ET, such as the catheter placement, the loading of the catheter, the speed of injection, the operation of catheter withdrawal and the uterine contraction –4. Due tBecause of practical restrictions and ethical issues, it is often difficult to perform an in vivo study in humans to monitor the motions and delivery sites of embryos during ET. Furthermore, even reported in vivo studies sometimes show contradictory results as mentioned above. Alternatively, mathematical modeling is a powerful tool for simulating and investigating the kinetic features of embryos in ET, and several models have been developed in the last decade. Yaniv et al. proposed a computational model to simulate ET within the uterine cavity and investigated the motions of embryos, where a two dimensional channel with oscillating walls was employed to represent the uterine peristalsis . FurtherThough the above models considered many important parameters during the ET procedures, an obvious drawback of them is that the transferred medium was assumed to have the same properties as the uterine fluid, which is often not true in real practice. Therefore, it is necessary to study the influence of the transferred medium. In this paper, a computational model for simulating the intrauterine mixing flow is developed to evaluate how the viscosity of the transferred medium affects the transport of embryos during ET. In particular, a homogeneous multiphase model is adopted in order to simulate the mixing flow in uterine cavity and a particle tracking technique is employed to predict the trajectories of the embryos. In the next section, the model and the numerical methods used are presented in detail, followed by the simulation results and discussion. Conclusion and recommendation of the optimal condition for real ET procedures considering the parameters studied in this work are given at the end.A two-dimensional region is established to represent the mid-sagittal cross-section of an average sized uterine cavity, which is shown in Fig. p is the pressure, ρm, μm and α, is calculated in the computational domain and used to distinguish the transferred medium and uterine fluid in a control volume. Since the time of embryo injection is very short during ET, the intrauterine flow is dominated by convective flow, whereas diffusion between the transferred medium and the uterine fluid is negligible and thus is ignored in this work. Because of the miscibility of the transferred medium and the uterine fluid, it is reasonable to assume that the velocities of the two species of fluids are equal locally. Therefore, the volume fraction equation of transferred medium can be expressed asα and ρ1 are the volume fraction and density of the transferred medium, respectively. To close Eqs. ) are) are3)) Our simulations mimic two consecutive processes during ET, embryo injection followed by catheter withdrawal. The simulation settings for both processes are described as follows.ρ2 = 1259.9 kg/m3 and viscosity μ2 = 0.799 Pa·s. The focus of our study is to examine the influence of the viscosity of the transferred medium on the intrauterine fluid flow and the deposition site of embryo during ET. Therefore, the viscosity of the transferred medium is tuned from 0.001 Pa·s  to 0.799 Pa·s (the viscosity of uterine fluid). Table μ1 = 0.001 Pa·s and ρ1 = 1000 kg/m3 is defined as the reference case  are depicted and the final deposition sites of all embryos are marked in Fig. x)  and the trajectories of e3 and e6 are reversed towards the cervix due to the circulation of vortices formed near the catheter tip  rotate along the vortex and travel towards the fundus, while other embryos (e1–e6) move to the outline of the dispersion pattern and five of them (e2–e6) fall into the upstream region  Fig. . After ttip Fig. . At the ion Fig. .Fig. 3Die9 and e10) are transported inside the vortices and they whirl in small areas within the vortices. On the other hand, the embryos initially close to the catheter axis (e.g. e1) travel further away from the catheter tip and towards the fundus  are shown in Fig. μ1 = 0.001 Pa·s) has a shape of an incomplete ellipse similar to that of the reference case, yet no embryos travel within the vortices due to the decreased incidence of vortex with slow injection speed. All the embryos are delivered near the outline of the dispersion pattern at the end of injection, and six of them falls in the upstream region  and embryo trajectories from the end of injection (t = 1 s) to the end of catheter withdrawal (t = 6 s) are depicted for the reference case  are significantly affected by the catheter withdrawal. Especially, the embryo (i.e. e6) nearest to the catheter wall at the end of injection is dragged out of the uterine cavity and into the cervix , nearly half of the embryos tracked in the simulations are delivered into the upstream regions (Case 1–4, Figs. Last but not least, our work shows that the delivery of embryos during ET also depends on catheter withdrawal, the successive procedure of embryo injection. According to the simulation results, all embryos are dragged back towards the cervix from their injected positions caused by catheter withdrawal Fig. . For theIn summary, a computational model is developed to simulate the intrauterine mixing flow and embryo trajectories during embryo injection and catheter withdrawal of ET. The simulation results show that the dispersion pattern of the transferred medium and the final delivery sites of the embryos are significantly influenced by the viscosity of the transferred medium. Specifically, increasing the transferred medium viscosity close to that of the uterine fluid can enhance the probability of the embryos arriving at the fundus and keep them from being dragged backward to the cervix by catheter withdrawal. Based on our work, the protocol that uses a transferred medium with similar viscosity to that of the uterine fluid and a slow injection speed is the optimal condition, and thus should be recommended for real ET procedures in clinic.


The appearance of multidrug‐resistant pathogens is a major threat to human health with the reemergence of fatal and untreatable diseases. In addition to a rational use of the well‐known and available antibiotics, two complementary ways to overcome this public health issue are (i) the discovery of new antimicrobials and (ii) the chemical modification of pre‐existing potent antibiotics. In this article, we highlight some of the strategies to generate new and promising antimicrobials for use in the management of these so‐called ‘superbugs’. Streptococcus and Staphylococcus and had great relevance in the victory of the Allied forces during the Second World War. The isolation of streptomycin to combat tuberculosis infections, the large‐scale production of antibiotics and the discoveries of the main families of antimicrobials used today are additional achievements that defined the so‐called Golden Age of Antibiotics . Examples include Pseudomonas aeruginosa or Acinetobacter baumannii strains that are responsible for multiple nosocomial diseases and are resistant to β‐lactams, such as carbapenems or third‐generation cephalosporins  a CBP disaccharide modification that enables the direct inhibition of the transglycosylase reaction without the need to bind to D‐Ala‐D‐Ala/D‐Ala‐D‐Lac; and (iii) the C1 quaternary ammonium salt C‐terminal modification responsible for membrane permeability. The result is a modified vancomycin molecule with the most potent inhibition of cell wall synthesis and the most pronounced and potent induction of cell membrane permeability, of all the compounds examined to date, with up to 10 000‐fold more potency than the original vancomycin (Okano et al., The conversion of In summary, the discovery of new antibiotics to address multidrug pathogenic bacteria is critical for human health, and our ability to be successful requires novel and creative screening strategies along with economic support and social awareness. New experimental and screening approaches are promisingly leading to the discovery of new antimicrobial compounds such as teixobactin and pseudouridimycin. On the other hand, as illustrated with vancomycin, well‐established chemical modification protocols may alternatively contribute to the diversification and strengthening of the potency of natural molecules. Finally, the two strategies together are foreseen to expand our capacity to generate novel and more successful molecules for the treatment of diseases caused by multidrug‐resistant bacteria.None declared.


Market timing is an investment technique that tries to continuously switch investment into assets forecast to have better returns. What is the likelihood of having a successful market timing strategy? With an emphasis on modeling simplicity, I calculate the feasible set of market timing portfolios using index mutual fund data for perfectly timed (by hindsight) all or nothing quarterly switching between two asset classes, US stocks and bonds over the time period 1993–2017. The historical optimal timing path of switches is shown to be indistinguishable from a random sequence. The key result is that the probability distribution function of market timing returns is asymmetric, that the highest probability outcome for market timing is a below median return. Put another way, simple math says market timing is more likely to lose than to win—even before accounting for costs. The median of the market timing return probability distribution can be directly calculated as a weighted average of the returns of the model assets with the weights given by the fraction of time each asset has a higher return than the other. For the time period of the data the median return was close to, but not identical with, the return of a static 60:40 stock:bond portfolio. These results are illustrated through Monte Carlo sampling of timing paths within the feasible set and by the observed return paths of several market timing mutual funds. Market timing is an investment technique whereby an investment manager  attempts to anticipate the price movement of asset classes of securities, such as stocks and bonds, and to switch investment money away from assets with lower anticipated returns into assets with higher anticipated returns. Market timing managers use economic or other data to calculate propitious times to switch. Market timing seems a popular approach to investment management, with Morningstar listing several hundred funds in its tactical asset allocation (TAA) category—TAA being an industry name for market timing—and mainstream fund managers advertising their ability to switch to defensive assets when stock markets seem poised for a downturn. The antithesis of market timing, and another broadly popular investing approach, is buy-and-hold, whereby investment managers allocate static fractions of their monies to the available asset classes and then ignore market price gyrations.Is market timing likely to be successful relative to investing in a static allocation to the available asset classes? The literature in this area is focused on developing sophisticated statistical tools that can detect and measure the market timing ability of professional fund managers . NumerouMy goal here is both different and simpler than statistical tests to detect market timing. I want to create a simple model to ask the question, what is the likelihood of successful market timing? Or more precisely, what is the return probability distribution function (PDF) for market timing? Is the PDF of market timing returns symmetric? If it is hard to obtain above average returns by market timing, is it also hard to obtain below average returns? What is the most basic mathematics of market timing?I try in this paper to evoke a similar spirit to Sharpe’s “The Arithmetic of Active Management” , in whicwww.nist.gov) suite of tests for randomness shows is indistinguishable from a random sequence. The key elementary result is that the geometric mean of market timing returns has an asymmetric PDF. One implication of this is that the most probable market timing return is below the median return, which can be directly calculated to be given by a static portfolio weighted by the relative fraction of time periods that each asset class outperforms the other. These results are illustrated through Monte Carlo sampling of timing paths within the feasible set and by the return paths of several market timing funds with comparably long, publicly available data. To begin, in the next section I describe the data.In the rest of the paper my approach will be to calculate the boundaries of the feasible set of market timing portfolios using fund data for perfectly timed (by hindsight) switching between two asset classes, stocks and bonds. From this analysis I also obtain the historically optimal timing path of switches, which the NIST  I reveal the optimal (highest possible return) timing sequence and test it for randomness. A later section focuses on deriving the return PDF for the model.ith time period ti the return of stocks is denoted rsi and the return of bonds is denoted rbi. A timing path is the binary sequence fi that isf is set to f = 1 when the stock return is larger than the bond return and set to f = 0 when the bond return is larger than the stock return. A special class of timing path has f = constant and is termed a static allocation or buy-and-hold portfolio. I call a return path, denoted ρ, the sequence of returns generated by a particular timing path fi. The jth return path is given byThe model consists of quarterly all or nothing switches between stocks and bonds. In the ρb and worst ρw possible return pathsρb is given by fb = (stocks > bonds); similarly for ρw. ρb and ρw, while ρb, and ρw. There are no surprises: partitioning returns by ρb, while excluding the negative return, left tail. The reverse happens to ρw.With perfect hindsight the best and worst performing return paths are easily found. In the notation of Matlab code f = 1), bonds (f = 0) and balanced (f = 0.6). The returns of the fixed portfolios are ordered as expected with f = 0 producing the lowest returns of the fixed f portfolios and f = 1 producing the highest. Note, however, that the large difference in returns normally associated with stocks and bonds is dwarfed by the difference in returns between the best and worst market timing portfolios. The potential reward to successful market timing is clearly enormous; however, just as enormous is the potential penalty to unsuccessful market timing.fi) fall inside the envelope made by ρb and ρw. As the model has all or nothing switches, the number of possible paths of length N is 2N. As the data set has N = 99, the number of possible return paths is 299 ∼ 1029, which is large.The best and worst possible return paths demark the feasible set of return paths for the two asset model. All possible return paths . White regions have fi = 0 (bond return > stock return). It will be convenient to define p as the fraction of time periods in which f = 1, which is easily calculated by summing fb and dividing by N. For this data p = pb ≈ 0.64: over this time period approximately 2/3 of the time stocks returned more than bonds. While the optimal timing path fb is not random like a coin flip (pb ≠ 1/2), fb random?pb is not known a priori—in fact pb could be different over different time periods or markets—the unpredictable die analogy holds for all pb by changing the number of sides to the die.It is worth distinguishing random and unpredictable. The historically optimal timing path is not a random bit sequence because ones occur about two-thirds of the time. Nonetheless, the important question is can I predict the next element in the sequence, given knowledge of the previous elements of the sequence? How can a sequence be not random but at the same time unpredictable? Consider a 6-sided die, of which four sides have a one and two sides have a zero. For each fair roll of the die there is a two-thirds probability of a one and a one-third probability of a zero, i.e. the chance of a 1 or 0 is similar to that observed in the data. Since each fair roll of the die is independent of all rolls that have come before, there is no way to predict from the past sequence of rolls what the next roll of the die will produce. Although N = 99 bit length of fb is close to the suggested minimum length. Again, leaving details to fb is random (unpredictable) at the 99% confidence level.Leaving the details to fb is clearly special in some sense—the probability of that particular sequence to occur is 2−99—the question is what, if anything, distinguishes fb from any other random timing paths? If we look at fb and randomly generated timing paths without knowing which is which, can we distinguish fb from the masses of possible timing paths? If fb is random, as the NIST tests say it is, there is nothing to tell why it is special, which says that it is not special, that just by a 2−99 random chance, it was special for this time period and that, in itself, fb is unpredictable, i.e. it contains no information about any future optimal timing path.While the historically optimal timing sequence f = 0.6 balanced index fund.As the optimal timing path is indistinguishable from a random sequence, I review elementary properties of random multiplicative processes, from which it follows that the highest probability outcome of market timing is a return less than the median of the PDF of market timing returns. The return PDF is estimated by Monte Carlo sampling of random timing paths. The median of the return PDF can be directly calculated as the weighted average of the returns of the assets with the weights given by the fraction of time each asset has a higher return than the other. For the time period covered by the data the median return was close to the M random timing paths of length N and calculate M return paths with p for the M timing paths is set to p = pb. This is done by using Matlab’s rand function to generate a length N sequence of random real numbers n drawn from a uniform distribution in the range  and setting each term in the sequence equal to one if n < pb or to zero if n ≥ pb. M = 105 return paths as thin gray lines in a semi-log plot similar to ρb and ρw, while the thick black line is the data for the f = 0.6 balanced fund. Before further examination of the return PDF it will be useful to review several facts about distributions from random multiplicative processes, such as that of The distribution of typical returns of the model can be estimated by Monte Carlo methods. Generate sum of random numbers is guaranteed by the central limit theorem to converge to a Gaussian  PDF in the limit of a large number of terms in the sum. A product of random numbers, such as that used in M and, until M approaches the number of possible outcomes, becomes larger and larger compared to the mode [A the mode .μ and σ are respectively the median and variance of the Gaussian PDF, then eμ is the median and eμ − σ2 is the mode of the log-normal PDF: the mode, which is the most probable outcome, is less than the median of the log-normal PDF. Thus from elementary considerations the most probable outcome from market timing is a return that is less than the median of the return PDF.Nonetheless, what can be done is to take the log of the geometric mean of M = 105 grossly under samples the order 1029 distinct paths in the feasible set, convergence to a Gaussian PDF is evident, as predicted by the form of ρw and ρb. The orange bar marks the median log-return and the log -return for the f = 0.6 balanced index fund, which are indistinguishable in this plot, and the reason for this will be discussed in the next section. To illustrate, E gives the most probable value of a PDF. After a calculation given in detail in μ of the log return distribution ispb is the observed fraction of time periods that the stock return exceeds the bond return. The median of the distribution of log returns is given by the log of the weighted average of the two assets with the weights given by the fraction of time periods p that each asset’s return exceeded that of the other. The median of the return PDF is eμ.The expectation value operator pb ≈ 0.64, that using the log return for the f = 0.6 balanced fund for the right hand side of ρb, which, of course, cannot be known a priori. As noted above, in f = 0.6 balanced index fund are indistinguishable at the scale of the plot.Note that because over the time period of the data costless market timing. In practice, market timing costs higher than the index fund costs would shift the PDF to the left, but the boundaries of the feasible set and the median of the PDF would not shift because they are calculated from fund data, which already includes the small index funds costs. In practice what the Monte Carlo simulation estimates is the lower bound of the most likely shortfall of market timing to the median return given by the appropriately weighted static portfolio.It is important to note that f sequences) is not representative of actual market timing. There are two answers to this. One is that the feasible set is well-defined and that it is simply a fact that all market timing paths, no matter how they are generated, are contained in the feasible set. As such, any sampling of the feasible set generates valid timing paths. The second answer is in Several critiques could be leveled at the analysis in this paper. For example, adherents of market timing would claim that their timing systems are not random, therefore they would be able to choose timing paths to have returns far out on the right tail of the PDF, i.e. that the strategy to generate random paths Click here for additional data file.S1 AppendixFund data scrapped from Yahoo Finance on 2 November 2017; applicable terms of service were complied with.(PDF)Click here for additional data file.S2 AppendixThe NIST test suite  consists(PDF)Click here for additional data file.S3 Appendix(PDF)Click here for additional data file.S4 AppendixFund data and objectives summaries scrapped from Yahoo Finance 6 November 2017; applicable terms of service were complied with.(PDF)Click here for additional data file.