Automatic Text Summarization by Providing Coverage, Non-Redundancy, and Novelty Using Sentence Graph

The day-to-day growth of online information necessitates intensive research in automatic text summarization (ATS). The ATS software produces summary text by extracting important information from the original text. With the help of summaries, users can easily read and understand the documents of interest. Most of the approaches for ATS used only local properties of text. Moreover, the numerous properties make the sentence selection difficult and complicated. So this article uses a graph based summarization to utilize structural and global properties of text. It introduces maximal clique based sentence selection (MCBSS) algorithm to select important and non-redundant sentences that cover all concepts of the input text for summary. The MCBSS algorithm finds novel information using maximal cliques (MCs). The experimental results of recall oriented understudy for gisting evaluation (ROUGE) on Timeline dataset show that the proposed work outperforms the existing graph algorithms Bushy Path (BP), Aggregate Similarity (AS), and TextRank (TR).

Structural Parameterizations of Clique Coloring

A clique coloring of a graph is an assignment of colors to its vertices such that no maximal clique is monochromatic. We initiate the study of structural parameterizations of the Clique Coloring problem which asks whether a given graph has a clique coloring with q colors. For fixed $$q \ge 2$$ q ≥ 2 , we give an $$\mathscr {O}^{\star }(q^{{\mathsf {tw}}})$$ O ⋆ ( q tw ) -time algorithm when the input graph is given together with one of its tree decompositions of width $${\mathsf {tw}} $$ tw . We complement this result with a matching lower bound under the Strong Exponential Time Hypothesis. We furthermore show that (when the number of colors is unbounded) Clique Coloring is $$\mathsf {XP}$$ XP parameterized by clique-width.

Quantum Walk on the Generalized Birkhoff Polytope Graph

We study discrete-time quantum walks on generalized Birkhoff polytope graphs (GBPGs), which arise in the solution-set to certain transportation linear programming problems (TLPs). It is known that quantum walks mix at most quadratically faster than random walks on cycles, two-dimensional lattices, hypercubes, and bounded-degree graphs. In contrast, our numerical results show that it is possible to achieve a greater than quadratic quantum speedup for the mixing time on a subclass of GBPG (TLP with two consumers and m suppliers). We analyze two types of initial states. If the walker starts on a single node, the quantum mixing time does not depend on m, even though the graph diameter increases with it. To the best of our knowledge, this is the first example of its kind. If the walker is initially spread over a maximal clique, the quantum mixing time is O(m/ϵ), where ϵ is the threshold used in the mixing times. This result is better than the classical mixing time, which is O(m1.5/ϵ).

Tight Bounds on the Clique Chromatic Number

The clique chromatic number of a graph is the minimum number of colours needed to colour its vertices so that no inclusion-wise maximal clique which is not an isolated vertex is monochromatic. We show that every graph of maximum degree $\Delta$ has clique chromatic number $O\left(\frac{\Delta}{\log~\Delta}\right)$. We obtain as a corollary that every $n$-vertex graph has clique chromatic number $O\left(\sqrt{\frac{n}{\log ~n}}\right)$. Both these results are tight.

Both Simulation and Sequencing Data Reveal Multiple SARS-CoV-2 Variants Coinfection in COVID-19 Pandemic

SARS-CoV-2 is a single-stranded RNA betacoronavirus with a high mutation rate. The rapidly emerged SARS-CoV-2 variants could increase the transmissibility, aggravate the severity, and even fade the vaccine protection. Although the coinfections of SARS-CoV-2 with other respiratory pathogens have been reported, whether multiple SARS-CoV-2 variants coinfection exists remains controversial. This study collected 12,986 and 4,113 SARS-CoV-2 genomes from the GISAID database on May 11, 2020 (GISAID20May11) and April 1, 2021 (GISAID21Apr1), respectively. With the single-nucleotide variants (SNV) and network clique analysis, we constructed the single-nucleotide polymorphism (SNP) coexistence networks and noted the SNP number of the maximal clique as the coinfection index. The coinfection indices of GISAID20May11 and GISAID21Apr1 datasets were 16 and 34, respectively. Simulating the transmission routes and the mutation accumulations, we discovered the linear relationship between the coinfection index and the coinfected variant number. Based on the linear relationship, we deduced that the COVID-19 cases in the GISAID20May11 and GISAID21Apr1 datasets were coinfected with 2.20 and 3.42 SARS-CoV-2 variants on average. Additionally, we performed Nanopore sequencing on 42 COVID-19 patients to explore the virus mutational characteristics. We found the heterozygous SNPs in 41 COVID-19 cases, which support the coinfection of SARS-CoV-2 variants and challenge the accuracy of phylogenetic analysis. In conclusion, our findings reported the coinfection of SARS-CoV-2 variants in COVID-19 patients, demonstrated the increased coinfected variants number in the epidemic, and provided clues for the prolonged viral shedding and severe symptoms in some cases.

The Action of the Weyl Group on the $$E_8$$ Root System

Let $$\varGamma $$ Γ be the graph on the roots of the $$E_8$$ E 8 root system, where any two distinct vertices e and f are connected by an edge with color equal to the inner product of e and f. For any set c of colors, let $$\varGamma _c$$ Γ c be the subgraph of $$\varGamma $$ Γ consisting of all the 240 vertices, and all the edges whose color lies in c. We consider cliques, i.e., complete subgraphs, of $$\varGamma $$ Γ that are either monochromatic, or of size at most 3, or a maximal clique in $$\varGamma _c$$ Γ c for some color set c, or whose vertices are the vertices of a face of the $$E_8$$ E 8 root polytope. We prove that, apart from two exceptions, two such cliques are conjugate under the automorphism group of $$\varGamma $$ Γ if and only if they are isomorphic as colored graphs. Moreover, for an isomorphism f from one such clique K to another, we give necessary and sufficient conditions for f to extend to an automorphism of $$\varGamma $$ Γ , in terms of the restrictions of f to certain special subgraphs of K of size at most 7.

Identification of potential biomarkers for pathogenesis of Alzheimer’s disease

Background Alzheimer’s disease (AD) is an extremely complicated neurodegenerative disorder, which accounts for almost 80 % of all dementia diagnoses. Due to the limited treatment efficacy, it is imperative for AD patients to take reliable prevention and diagnosis measures. This study aimed to explore potential biomarkers for AD. Methods GSE63060 and GSE140829 datasets were downloaded from the Gene Expression Omnibus (GEO) database. The differentially expressed genes (DEG) between AD and control groups in GSE63060 were analyzed using the limma software package. The mRNA expression data in GSE140829 was analyzed using weighted gene co-expression network analysis (WGCNA) function package. Protein functional connections and interactions were analyzed using STRING and key genes were screened based on the degree and Maximal Clique Centrality (MCC) algorithm. Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) enrichment analyses were performed on the key genes. Results There were 65 DEGs in GSE63060 dataset between AD patients and healthy controls. In GSE140829 dataset, the turquoise module was related to the pathogenesis of AD, among which, 42 genes were also differentially expressed in GSE63060 dataset. Then 8 genes, RPS17, RPL26, RPS3A, RPS25, EEF1B2, COX7C, HINT1 and SNRPG, were finally screened. Additionally, these 42 genes were significantly enriched in 12 KEGG pathways and 119 GO terms. Conclusions In conclusion, RPS17, RPL26, RPS3A, RPS25, EEF1B2, COX7C, HINT1 and SNRPG, were potential biomarkers for pathogenesis of AD, which should be further explored in AD in the future.

GraphMineSuite

We propose GraphMineSuite (GMS): the first benchmarking suite for graph mining that facilitates evaluating and constructing high-performance graph mining algorithms. First, GMS comes with a benchmark specification based on extensive literature review, prescribing representative problems, algorithms, and datasets. Second, GMS offers a carefully designed software platform for seamless testing of different fine-grained elements of graph mining algorithms, such as graph representations or algorithm subroutines. The platform includes parallel implementations of more than 40 considered baselines, and it facilitates developing complex and fast mining algorithms. High modularity is possible by harnessing set algebra operations such as set intersection and difference, which enables breaking complex graph mining algorithms into simple building blocks that can be separately experimented with. GMS is supported with a broad concurrency analysis for portability in performance insights, and a novel performance metric to assess the throughput of graph mining algorithms, enabling more insightful evaluation. As use cases, we harness GMS to rapidly redesign and accelerate state-of-the-art baselines of core graph mining problems: degeneracy reordering (by >2X), maximal clique listing (by >9×), k -clique listing (by up to 1.1×), and subgraph isomorphism (by 2.5×), also obtaining better theoretical performance bounds.

Hyaluronan-mediated motility receptor expression functions as a prognostic biomarker in uterine carcinosarcoma based on bioinformatics analysis

Objective Uterine carcinosarcoma (UCS) is a rare, aggressive tumour with a high metastasis rate and poor prognosis. This study aimed to explore potential key genes associated with the prognosis of UCS. Methods Transcriptional expression data were downloaded from the Gene Expression Profiling Interactive Analysis database and differentially expressed genes (DEGs) were subjected to Gene Ontology and Kyoto Encyclopedia of Genes and Genomes analyses using Metascape. A protein–protein interaction network was constructed using the STRING website and Cytoscape software, and the top 30 genes obtained through the Maximal Clique Centrality algorithm were selected as hub genes. These hub genes were validated by clinicopathological and sequencing data for 56 patients with UCS from The Cancer Genome Atlas database. Results A total of 1894 DEGs were identified, and the top 30 genes were considered as hub genes. Hyaluronan-mediated motility receptor (HMMR) expression was significantly higher in UCS tissues compared with normal tissues, and elevated expression of HMMR was identified as an independent prognostic factor for shorter survival in patients with UCS. Conclusions These results suggest that HMMR may be a potential biomarker for predicting the prognosis of patients with UCS.