Spanning subgraph with Eulerian components

AbstractA graph is k-supereulerian if it has a spanning even subgraph with at most k components. We show that if G is a connected graph and G′ is the (collapsible) reduction of G, then G is k-supereulerian if and only if G′ is k-supereulerian. This extends Catlin’s reduction theorem in [P.A. Catlin, A reduction method to find spanning Eulerian subgraphs, J. Graph Theory 12 (1988) 29–44]. For a graph G, let F(G) be the minimum number of edges whose addition to G create a spanning supergraph containing two edge-disjoint spanning trees. We prove that if G is a connected graph with F(G)≤k, where k is a positive integer, then either G is k-supereulerian or G can be contracted to a tree of order k+1. This is a best possible result which extends another theorem of Catlin, in [P.A. Catlin, A reduction method to find spanning Eulerian subgraphs, J. Graph Theory 12 (1988) 29–44]. Finally, we use these results to give a sufficient condition on the minimum degree for a graph G to bek-supereulerian

Layer-wise Representation Fusion for Compositional Generalization

Despite successes across a broad range of applications, sequence-to-sequence models' construct of solutions are argued to be less compositional than human-like generalization. There is mounting evidence that one of the reasons hindering compositional generalization is representations of the encoder and decoder uppermost layer are entangled. In other words, the syntactic and semantic representations of sequences are twisted inappropriately. However, most previous studies mainly concentrate on enhancing token-level semantic information to alleviate the representations entanglement problem, rather than composing and using the syntactic and semantic representations of sequences appropriately as humans do. In addition, we explain why the entanglement problem exists from the perspective of recent studies about training deeper Transformer, mainly owing to the ``shallow'' residual connections and its simple, one-step operations, which fails to fuse previous layers' information effectively. Starting from this finding and inspired by humans' strategies, we propose \textsc{FuSion} (\textbf{Fu}sing \textbf{S}yntactic and Semant\textbf{i}c Representati\textbf{on}s), an extension to sequence-to-sequence models to learn to fuse previous layers' information back into the encoding and decoding process appropriately through introducing a \emph{fuse-attention module} at each encoder and decoder layer. \textsc{FuSion} achieves competitive and even \textbf{state-of-the-art} results on two realistic benchmarks, which empirically demonstrates the effectiveness of our proposal.Comment: work in progress. arXiv admin note: substantial text overlap with arXiv:2305.1216

Sleep and mental health during the COVID-19 pandemic: findings from an online questionnaire survey in China

IntroductionThe online study investigated the sleep, psychological conditions, and risk factors during the wave of transmission of COVID-19 since December 7, 2022.MethodsWe distributed questionnaires through networking mediums to residents to gather information about COVID-19 infection, sleep, and mental status.ResultsDuring the extraordinary period in China, 91.9% of 1094 participants claimed to be infected with COVID-19, 36.8% reported poor sleep quality, 75.9% reported anxiety, and 65.5% reported depression. In retrospect, people have experienced lower sleep quality, longer sleep latency, enhanced rising time, and decreased sleep efficiency after the infection wave. After adjusting confounding factors, the elderly, women, urban residents, people with comorbidity, anxiety, depression, stress state, and COVID-19 infection have high risks for sleep disorders during the period.DiscussionThe survey indicates that sleep disturbance caused by COVID-19 involves multiple dimensions, such as physiology, psychology, and society. The COVID-19 infection-related sleep problem should be taken seriously. Apart from conventional treatment, psychological issues of insomnia can not be ignored

Retrospective evaluation of whole exome and genome mutation calls in 746 cancer samples

Funder: NCI U24CA211006Abstract: The Cancer Genome Atlas (TCGA) and International Cancer Genome Consortium (ICGC) curated consensus somatic mutation calls using whole exome sequencing (WES) and whole genome sequencing (WGS), respectively. Here, as part of the ICGC/TCGA Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium, which aggregated whole genome sequencing data from 2,658 cancers across 38 tumour types, we compare WES and WGS side-by-side from 746 TCGA samples, finding that ~80% of mutations overlap in covered exonic regions. We estimate that low variant allele fraction (VAF < 15%) and clonal heterogeneity contribute up to 68% of private WGS mutations and 71% of private WES mutations. We observe that ~30% of private WGS mutations trace to mutations identified by a single variant caller in WES consensus efforts. WGS captures both ~50% more variation in exonic regions and un-observed mutations in loci with variable GC-content. Together, our analysis highlights technological divergences between two reproducible somatic variant detection efforts

Towards automatic traffic classification and estimation of available bandwidth in IP networks

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