Graphs with many valencies and few eigenvalues

Dom de Caen posed the question whether connected graphs with three distinct eigenvalues have at most three distinct valencies. We do not answer this question, but instead construct connected graphs with four and five distinct eigenvalues and arbitrarily many distinct valencies. The graphs with four distinct eigenvalues come from regular two-graphs. As a side result, we characterize the disconnected graphs and the graphs with three distinct eigenvalues in the switching class of a regular two-graph

Rare dental trait provides morphological evidence of archaic introgression in Asian fossil record

The recently described Denisovan hemimandible from Xiahe, China [F. Chen et al., (2019) Nature 569, 409–412], possesses an unusual dental feature: a 3-rooted lower second molar. A survey of the clinical and bioarchaeological literature demonstrates that the 3-rooted lower molar is rare (less than 3.5% occurrence) in non-Asian Homo sapiens. In contrast, its presence in Asian-derived populations can exceed 40% in China and the New World. It has long been thought that the prevalence of 3-rooted lower molars in Asia is a relatively late acquisition occurring well after the origin and dispersal of H. sapiens. However, the presence of a 3-rooted lower second molar in this 160,000-y-old fossil hominin suggests greater antiquity for the trait. Importantly, it also provides morphological evidence of a strong link between archaic and recent Asian H. sapiens populations. This link provides compelling evidence that modern Asian lineages acquired the 3-rooted lower molar via introgression from Denisovans

Jet Physics at the Tevatron

Recent analyses by the CDF and D0 Collaborations of jet data produced in proton-antiproton collisions at the Fermilab Tevatron Collider are presented. These include new studies of the inclusive jet production cross section, a measurement of the strong coupling constant, the first measurement of subjet multiplicity of quark and gluon jets, examination of ratios of multijet cross sections and their implications for choice of renormalization scale, and a study of charged jet evolution and energy flow in the underlying event. The results are compared to theoretical predictions.Comment: Proceedings of the XXXVII Rencontres de Moriond: QCD and High Energy Hadronic Interaction

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