Hamiltonian unknottedness of certain monotone Lagrangian tori in S2× S2

Lagrangian unknottedness in Stein surfaces

We show that the space of Lagrangian spheres inside the cotangent bundle of the 2-sphere is contractible. We then discuss the phenomenon of Lagrangian unknottedness in other Stein surfaces. There exist homotopic Lagrangian spheres which are not Hamiltonian isotopic, but we show that in a typical case all such spheres are still equivalent under a symplectomorphism.

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Empirical density plots (Fig A to J) suggest that π̂IBD for pairs of parasite samples within and across clinics loosely follow a mixture distribution over three classes: 1) near zero π̂IBD shown in green; 2) low to intermediate π̂IBD shown in shades of blue; and 3) high π̂IBD, which notably rarefies with distance, and is colored red if sufficiently dense to be visible, and otherwise outlined in bla...

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All tools used in the online tutorial (www.rnaseq.wiki) are referenced below (in bold) along with alternative tools in each category. Where possible a citation is provided. Links are also provided to help the user evaluate the code and the level of maintenance. Where possible the link goes directly to a source controlled repository such as a git repo. Additional lists of tools can be found here...

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The nomenclature used here (see also Fig. S1) was built on classical dental serial homologies. The work of Hershkovitz [2] was a major source for defining homologous structures and naming them, but other sources were also considered [3-7]. These works emphasized dental structures that are expressed as relief on tooth crowns. Structures expressed as depressions, in particular groove systems, wer...

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