Locally-iterative Distributed (Δ + 1)-coloring and Applications

We consider graph coloring and related problems in the distributed message-passing model. Locally-iterative algorithms are especially important in this setting. These are algorithms in which each vertex decides about its next color only as a function of the current colors in its 1-hop-neighborhood . In STOC’93 Szegedy and Vishwanathan showed that any locally-iterative Δ + 1-coloring algorithm requires Ω (Δ log Δ + log * n ) rounds, unless there exists “a very special type of coloring that can be very efficiently reduced” [ 44 ]. No such special coloring has been found since then. This led researchers to believe that Szegedy-Vishwanathan barrier is an inherent limitation for locally-iterative algorithms and to explore other approaches to the coloring problem [ 2 , 3 , 19 , 32 ]. The latter gave rise to faster algorithms, but their heavy machinery that is of non-locally-iterative nature made them far less suitable to various settings. In this article, we obtain the aforementioned special type of coloring. Specifically, we devise a locally-iterative Δ + 1-coloring algorithm with running time O (Δ + log * n ), i.e., below Szegedy-Vishwanathan barrier. This demonstrates that this barrier is not an inherent limitation for locally-iterative algorithms. As a result, we also achieve significant improvements for dynamic, self-stabilizing, and bandwidth-restricted settings. This includes the following results: We obtain self-stabilizing distributed algorithms for Δ + 1-vertex-coloring, (2Δ - 1)-edge-coloring, maximal independent set, and maximal matching with O (Δ + log * n ) time. This significantly improves previously known results that have O(n) or larger running times [ 23 ]. We devise a (2Δ - 1)-edge-coloring algorithm in the CONGEST model with O (Δ + log * n ) time and O (Δ)-edge-coloring in the Bit-Round model with O (Δ + log n ) time. The factors of log * n and log n are unavoidable in the CONGEST and Bit-Round models, respectively. Previously known algorithms had superlinear dependency on Δ for (2Δ - 1)-edge-coloring in these models. We obtain an arbdefective coloring algorithm with running time O (√ Δ + log * n ). Such a coloring is not necessarily proper, but has certain helpful properties. We employ it to compute a proper (1 + ε)Δ-coloring within O (√ Δ + log * n ) time and Δ + 1-coloring within O (√ Δ log Δ log * Δ + log * n ) time. This improves the recent state-of-the-art bounds of Barenboim from PODC’15 [ 2 ] and Fraigniaud et al. from FOCS’16 [ 19 ] by polylogarithmic factors. Our algorithms are applicable to the SET-LOCAL model [ 25 ] (also known as the weak LOCAL model). In this model a relatively strong lower bound of Ω (Δ 1/3 ) is known for Δ + 1-coloring. However, most of the coloring algorithms do not work in this model. (In Reference [ 25 ] only Linial’s O (Δ 2 )-time algorithm and Kuhn-Wattenhofer O (Δ log Δ)-time algorithms are shown to work in it.) We obtain the first linear-in-Δ Δ + 1-coloring algorithms that work also in this model.

Algorithms for Weighted Independent Transversals and Strong Colouring

An independent transversal (IT) in a graph with a given vertex partition is an independent set consisting of one vertex in each partition class. Several sufficient conditions are known for the existence of an IT in a given graph and vertex partition, which have been used over the years to solve many combinatorial problems. Some of these IT existence theorems have algorithmic proofs, but there remains a gap between the best existential bounds and the bounds obtainable by efficient algorithms. Recently, Graf and Haxell (2018) described a new (deterministic) algorithm that asymptotically closes this gap, but there are limitations on its applicability. In this article, we develop a randomized algorithm that is much more widely applicable, and demonstrate its use by giving efficient algorithms for two problems concerning the strong chromatic number of graphs.

Metabolic and proteomic signatures of type 2 diabetes subtypes in an Arab population

Background. Type 2 diabetes (T2D) has a heterogeneous etiology which is increasingly recognized to influence the risk of complications and choice of treatment. A data driven cluster analysis in four separate European populations of patients with type 2 diabetes identified four subtypes of severe insulin dependent (SIDD), severe insulin resistant (SIRD), mild obesity-related (MOD), and mild age-related (MARD) (Ahlqvist et al., Lancet Diabetes Endocrinology, 2018). Our aim was to extend this classification to the Arab population of Qatar and characterize the biological processes that differentiate these subtypes in relation to metabolomic and proteomic signatures. Methods. The Ahlqvist et al. subtype clustering approach was applied to 631 individuals with T2D from the Qatar Biobank (QBB) and validated in an independent set of 420 participants from the same population. The association between blood metabolites (n=1,159) and protein levels (n=1,305) with each cluster were established. Findings. The four subtypes of T2D were reproduced and validated in the population of Qatar. Cluster-specific metabolomic and proteomic associations revealed subtype-specific molecular processes. Activation of the complement system with many features of autoimmune diabetes and reduced 1,5-anhydroglucitol (1,5-AG) characterized SIDD, with evidence of impaired insulin signaling in SIRD, elevated leptin and fatty acid binding protein in MOD, whilst MARD appeared to be the healthiest subgroup. Interpretation. We have replicated the four T2D clusters in an Arab population and identified distinct metabolic and proteomic signatures, providing insights into underlying etiology with the potential to deploy subtype-specific treatment options.

Mining the Wheat Grain Proteome

Bread wheat is the most widely cultivated crop worldwide, used in the production of food products and a feed source for animals. Selection tools that can be applied early in the breeding cycle are needed to accelerate genetic gain for increased wheat production while maintaining or improving grain quality if demand from human population growth is to be fulfilled. Proteomics screening assays of wheat flour can assist breeders to select the best performing breeding lines and discard the worst lines. In this study, we optimised a robust LC–MS shotgun quantitative proteomics method to screen thousands of wheat genotypes. Using 6 cultivars and 4 replicates, we tested 3 resuspension ratios (50, 25, and 17 µL/mg), 2 extraction buffers (with urea or guanidine-hydrochloride), 3 sets of proteases (chymotrypsin, Glu-C, and trypsin/Lys-C), and multiple LC settings. Protein identifications by LC–MS/MS were used to select the best parameters. A total 8738 wheat proteins were identified. The best method was validated on an independent set of 96 cultivars and peptides quantities were normalised using sample weights, an internal standard, and quality controls. Data mining tools found particularly useful to explore the flour proteome are presented (UniProt Retrieve/ID mapping tool, KEGG, AgriGO, REVIGO, and Pathway Tools).

Cancer-driving mutations are enriched in genic regions intolerant to germline variation

Large reference datasets of protein-coding variation in human populations have allowed us to determine which genes and genic sub-regions are intolerant to germline genetic variation. There is also a growing number of genes implicated in severe Mendelian diseases that overlap with genes implicated in cancer. Here, we hypothesized that mitotically mutable genic sub-regions that are intolerant to germline variation are enriched for cancer-driving mutations. We introduce a new metric, OncMTR, which uses 125,748 exomes in the gnomAD database to identify genic sub-regions intolerant to germline variation but enriched for hematologic somatic variants. We demonstrate that OncMTR can significantly predict driver mutations implicated in hematologic malignancies. Divergent OncMTR regions were enriched for cancer-relevant protein domains, and overlaying OncMTR scores on protein structures identified functionally important protein residues. Finally, we performed a rare variant, gene-based collapsing analysis on an independent set of 394,694 exomes from the UK Biobank and find that OncMTR dramatically improves genetic signals for hematologic malignancies. Our web app enables easy visualization of OncMTR scores for each protein-coding gene (https://astrazeneca-cgr-publications.github.io/OncMTR-Viewer/).

Identifying Multiple Influential Spreaders in Complex Networks by Considering the Dispersion of Nodes

Identifying multiple influential spreaders, which relates to finding k (k > 1) nodes with the most significant influence, is of great importance both in theoretical and practical applications. It is usually formulated as a node-ranking problem and addressed by sorting spreaders’ influence as measured based on the topological structure of interactions or propagation process of spreaders. However, ranking-based algorithms may not guarantee that the selected spreaders have the maximum influence, as these nodes may be adjacent, and thus play redundant roles in the propagation process. We propose three new algorithms to select multiple spreaders by taking into account the dispersion of nodes in the following ways: (1) improving a well-performed local index rank (LIR) algorithm by extending its key concept of the local index (an index measures how many of a node’s neighbors have a higher degree) from first-to second-order neighbors; (2) combining the LIR and independent set (IS) methods, which is a generalization of the coloring problem for complex networks and can ensure the selected nodes are non-adjacent if they have the same color; (3) combining the improved second-order LIR method and IS method so as to make the selected spreaders more disperse. We evaluate the proposed methods against six baseline methods on 10 synthetic networks and five real networks based on the classic susceptible-infected-recovered (SIR) model. The experimental results show that our proposed methods can identify nodes that are more influential. This suggests that taking into account the distances between nodes may aid in the identification of multiple influential spreaders.

Immunologic constant of rejection signature is prognostic in soft-tissue sarcoma and refines the CINSARC signature

BackgroundSoft-tissue sarcomas (STSs) are heterogeneous and aggressive tumors, with high metastatic risk. The immunologic constant of rejection (ICR) 20-gene signature is a signature of cytotoxic immune response. We hypothesized that ICR might improve the prognostic assessment of early-stage STS.MethodsWe retrospectively applied ICR to 1455 non-metastatic STS and searched for correlations between ICR classes and clinicopathological and biological variables, including metastasis-free survival (MFS).ResultsThirty-four per cent of tumors were classified as ICR1, 27% ICR2, 24% ICR3, and 15% ICR4. These classes were associated with patients’ age, pathological type, and tumor depth, and an enrichment from ICR1 to ICR4 of quantitative/qualitative scores of immune response. ICR1 class was associated with a 59% increased risk of metastatic relapse when compared with ICR2-4 class. In multivariate analysis, ICR classification remained associated with MFS, as well as pathological type and Complexity Index in Sarcomas (CINSARC) classification, suggesting independent prognostic value. A prognostic clinicogenomic model, including the three variables, was built in a learning set (n=339) and validated in an independent set (n=339), showing greater prognostic precision than each variable alone or in doublet. Finally, connectivity mapping analysis identified drug classes potentially able to reverse the expression profile of poor-prognosis tumors, such as chemotherapy and targeted therapies.ConclusionICR signature is independently associated with postoperative MFS in early-stage STS, independently from other prognostic features, including CINSARC. We built a robust prognostic clinicogenomic model integrating ICR, CINSARC, and pathological type, and suggested differential vulnerability of each prognostic group to different systemic therapies.