1,378 research outputs found

    Exhaustive generation of kk-critical H\mathcal H-free graphs

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    We describe an algorithm for generating all kk-critical H\mathcal H-free graphs, based on a method of Ho\`{a}ng et al. Using this algorithm, we prove that there are only finitely many 44-critical (P7,Ck)(P_7,C_k)-free graphs, for both k=4k=4 and k=5k=5. We also show that there are only finitely many 44-critical graphs (P8,C4)(P_8,C_4)-free graphs. For each case of these cases we also give the complete lists of critical graphs and vertex-critical graphs. These results generalize previous work by Hell and Huang, and yield certifying algorithms for the 33-colorability problem in the respective classes. Moreover, we prove that for every tt, the class of 4-critical planar PtP_t-free graphs is finite. We also determine all 27 4-critical planar (P7,C6)(P_7,C_6)-free graphs. We also prove that every P10P_{10}-free graph of girth at least five is 3-colorable, and determine the smallest 4-chromatic P12P_{12}-free graph of girth five. Moreover, we show that every P13P_{13}-free graph of girth at least six and every P16P_{16}-free graph of girth at least seven is 3-colorable. This strengthens results of Golovach et al.Comment: 17 pages, improved girth results. arXiv admin note: text overlap with arXiv:1504.0697

    Mining State-Based Models from Proof Corpora

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    Interactive theorem provers have been used extensively to reason about various software/hardware systems and mathematical theorems. The key challenge when using an interactive prover is finding a suitable sequence of proof steps that will lead to a successful proof requires a significant amount of human intervention. This paper presents an automated technique that takes as input examples of successful proofs and infers an Extended Finite State Machine as output. This can in turn be used to generate proofs of new conjectures. Our preliminary experiments show that the inferred models are generally accurate (contain few false-positive sequences) and that representing existing proofs in such a way can be very useful when guiding new ones.Comment: To Appear at Conferences on Intelligent Computer Mathematics 201

    A PCR Survey of Xenoturbella bocki Hox Genes

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    Xenoturbella bocki has recently been identified as one of the most basal deuterostomes, although an even more basal phylogenetic position cannot be ruled out. Here we report on a polymerase chain reaction survey of partial Hox homeobox sequences of X. bocki. Surprisingly, we did not find evidence for more than five Hox genes, one clear labial/PG1 ortholog, one posterior gene most similar to the PG9/10 genes of Ambulacraria, and three central group genes whose precise assignment to a specific paralog group remains open. We furthermore report on a re‐evaluation of the available published evidence of Hox genes in other basal deuterostomes

    Targeted analysis of polymorphic loci from low-coverage shotgun sequence data allows accurate genotyping of HLA genes in historical human populations

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    The highly polymorphic human leukocyte antigen (HLA) plays a crucial role in adaptive immunity and is associated with various complex diseases. Accurate analysis of HLA genes using ancient DNA (aDNA) data is crucial for understanding their role in human adaptation to pathogens. Here, we describe the TARGT pipeline for targeted analysis of polymorphic loci from low-coverage shotgun sequence data. The pipeline was successfully applied to medieval aDNA samples and validated using both simulated aDNA and modern empirical sequence data from the 1000 Genomes Project. Thus the TARGT pipeline enables accurate analysis of HLA polymorphisms in historical (and modern) human populations

    A Human-Oriented Term Rewriting System

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    © Springer Nature Switzerland AG 2019. We introduce a fully automatic system, implemented in the Lean theorem prover, that solves equality problems of everyday mathematics. Our overriding priority in devising the system is that it should construct proofs of equality in a way that is similar to that of humans. A second goal is that the methods it uses should be domain independent. The basic strategy of the system is to operate with a subtask stack: whenever there is no clear way of making progress towards the task at the top of the stack, the program finds a promising subtask, such as rewriting a subterm, and places that at the top of the stack instead. Heuristics guide the choice of promising subtasks and the rewriting process. This makes proofs more human-like by breaking the problem into tasks in the way that a human would. We show that our system can prove equality theorems simply, without having to preselect or orient rewrite rules as in standard theorem provers, and without having to invoke heavy duty tools for performing simple reasoning

    a descriptive study on familiarity with, adherence to and trust in the WHO preventive measures

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    Background Risk communication is a key component of public health interventions during an outbreak. As the coronavirus pandemic unfolded in late 2019, the World Health Organization (WHO) was at the forefront in the development of risk communication strategies. The WHO introduced a range of activities with the purpose of enabling the public to avail verified and timely information on COVID-19 prevention behaviors. Given the various WHO activities to protect the public health during COVID-19, it is important to investigate the extent of familiarity and uptake of the WHO recommendations among the public during the first wave of the pandemic. Methods To do this, we conducted a large-scale Pan-European survey covering around 7500 individuals that are representative of populations from seven European countries, collected online during April 2-April 15, 2020. We use descriptive statistics including proportions and correlations and graphical representations such as bar charts to analyze and display the data. Results Our findings suggest that information from the WHO in the context of COVID-19 is well trusted and acted upon by the public. Overall familiarity and adherence were quite high in most countries. Adherence was higher for social distancing recommendations compared to hygiene measures. Familiarity and adherence were higher among older, female, and highly educated respondents. However, country level heterogeneities were observed in the level of trust in information from the WHO, with countries severely affected by the pandemic reporting lower levels of trust. Conclusion Our findings call for efforts from health authorities to get regular feedback from the public on their familiarity and compliance with recommendations for preventive measures at all stages of the pandemic, to further develop and adapt risk communication as the pandemic evolves.publishersversionpublishe
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